Conf_inv_sampling_hypothesis.ipynb

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    "# Confidence interval, sampling, hypothesis testing\n",
    "### Dr. Tirthajyoti Sarkar, Fremont, CA 94536\n",
    "\n",
    "In this Notebook, we will examine a multitude of concepts,\n",
    "\n",
    "- confidence interval\n",
    "- sampling methods\n",
    "- Bootstrapping\n",
    "- hypothesis testing using James Bond example\n",
    "\n",
    "---"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "from scipy import mean"
   ]
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    "## Confidence interval\n",
    "<br>\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/Conf_interval.png\" width=600 height=420></img>\n",
    "\n",
    "**Source**: https://psu.instructure.com/courses/1844486/pages/chapter-3-confidence-intervals\n",
    "\n",
    "<br>\n",
    "Confidence intervals are a calculated range or boundary around a parameter or a statistic that is supported mathematically with a certain level of confidence. \n",
    "\n",
    "This is *__different__* than having a 95% probability that the true population proportion is within our confidence interval. Essentially, if we were to repeat this process, 95% of our calculated confidence intervals would contain the true proportion.\n",
    "\n",
    "The equation to create a confidence interval can also be shown as:\n",
    "\n",
    "$$Population\\ Proportion\\ or\\ Mean\\ \\pm (t-multiplier *\\ Standard\\ Error)$$\n",
    "\n",
    "The _Standard Error_ is calculated differenly for population proportion and mean:\n",
    "\n",
    "$$Standard\\ Error \\ for\\ Population\\ Proportion = \\sqrt{\\frac{Population\\ Proportion * (1 - Population\\ Proportion)}{Number\\ Of\\ Observations}}$$\n",
    "\n",
    "$$Standard\\ Error \\ for\\ Mean = \\frac{Standard\\ Deviation}{\\sqrt{Number\\ Of\\ Observations}}$$\n",
    "\n",
    "Or C.I. (**C**onfidence **I**nterval),\n",
    "\n",
    "$$ C.I. = \\mu \\pm t*\\frac{\\sigma}{\\sqrt{n}} $$\n",
    "\n",
    "where,\n",
    "\n",
    "$\\mu = \\text{sample mean}$, $\\sigma = \\text{sample standard dev}$, $n = \\text{number of samples}$"
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   "source": [
    "num_weeks = 52\n",
    "production = np.random.normal(loc=20,scale=5,size=num_weeks)"
   ]
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KOFV9TFVFVY9UKwUyTVVnqepkVR3vW/ap9Pavqup56devqOpR6Wmqqn4nybFH\nTVSiK6nsSSjdetDYaFa0zs6MKAtCLgHnz6D0i7EgZGdzevWmkiKsCxWiEXDZWajgMlErRTWVtKlG\n/O7TXGIhKGeeaSES8+ZF04rO+w7lskBFVQ/Ob30L8rcn5UYt5tJuaoLLL7fXzgqXLElb4BxpgpS2\naGiwqRCNjXDlldGNqxDlWA9KcaPmEnANDfZ02tlppv0weDfIQw+1edIWuHJcqKWWEunoyG09cC7U\nyhDke19fn9xDWbVRrvvUo7nZRBxEU2opXwwcxCPggpCUgAvyP/nUp2z+29+a9dSVxkkGJ+AqxMyZ\nxW/kffpYq5Lm5tzb9ukDd9+dXAxXOdaDqAQclO5G9Z7Ep02DxsZO3ngjuUKYUJqAK9cCt3Gjid0R\nI7peQ84CVxmCfO87OqzOV2+sFVduAoOfKOPg8rlQwQL5+/aF558v74EorIDztrv++nivjyAC7uWX\nbQwdHfYAX631SnsaTsBViEmTTHzlEmeNjbb87rvNNL1okWVLejfy5mbbbtAgOP305MZcTkHcOARc\n2EQG7wY5Zgy0tFj6ZZJu1ErEwOWKfwMXA1cpvO99rhZRjY0Zi/vnPmcV96u9gHfURGWBg4yAe+CB\n8jslFBJwffvCsem+QOU0tg8j4GbPtocBMNEU5/VR7H/iJbflCmlpb7ekt1zJbY7yCSXg0kkFM0Tk\nP0Xke1nT/8Q1yJ6KV9rCE2ciyqBB3UtbTJpk2ZLbtmWecKZNM+vKzTcnN94g1oN8Lt1ShEg+AVdq\nJqo/G3P06OQFXCkxcOW6ULMzUD2cC7VynHWWxQ2BWas968mMGbBkiYk3VRMd2TGnPf0HMUoBd8AB\nMHWqCZt//rO8fRWKgYOMG/Wxx8o/RjEB5wmmXbu6r4vj+ij2P3GlcSpHYAEnIv8OvAL8FPgY8N4c\nkyMkfnH2j388wrZtxUtbiMA3v2mvv/td2BOqmEt5Y/WshtmxeX6rYa6xV4ML1R/M7wm4JOPgKuFC\nzWeBcy7UyjF3rj2EHXywiYuODt783k+ebHUV64rcmXvqD2KULlSAd77T5uW4UTs67GEZut+LPKKI\ngwsq4JIUTEHKurjSOJUjjAXuv4AHgBZVHaeqE7OmiL5yjiC8+91mKl+3zprIJ4VnNXzPezLLclkN\ns6kmF2pLC4wZ0ztcqLkyUKE2XKg9NQbM69F51lm5199+e/EM6574g9jRAatW2esJE6LZpxfo/6Mf\nlX4NeRnvw4bl90BE0dg+qIBLUjC99poV+x4+PH9pE1cap3KEEXDjgR+rahXf8nsPdXXwjW/Y6//+\n7/JjPMIwaZI1MgY45xwCWQ0vuvX5AAAgAElEQVSjFHBRulArYYEL40IdONDcbTt2lHYDLGaBq1YX\naq6OHz0lBqyYgOutP4hr15r1cfTojIu5HGbPho99zF53dpZ+DRWKf/MYMaL8xvZBBVyS10cQl7Yr\njVM5wgi4J4BD4hqIIzwXXGCBzmvWwK23JnvsfLFV+YgyBi4aF6oFkFQiBi6MBU6kvDi4WnShFur4\nUesxYNu3w1NPWRJDvgSk3vqD6ImFKNyn/msom7DXUBABB+W7UYMKuCSvjyACrpzkNkd5hBFwXwRm\niMil6WSG5uwprkE6cuO3wv3Xf0XXmisI+Vxz+fBb4IL0DNy3z8SFSEaweZTiQt23z+JYREwQ1koM\nHJTnRq3FLNSeHBSdSpmr8IQTYPDg3Nv01h/EKBMYoryGiiUweCQl4JK8PoL8T8pJbnOURxgBtwg4\nArgFWAO05pgcCfPe95rpfuXKZGNiwlrgBgywaffuYAV4PXE2bFj3kguluFDfeMOE44gRloAxdGg7\nTU3mQgxbELhUPHdlGBcqZMRXORa4WspC7clB0Q88YPOzz86/TW/9QYwygSHKa6hQEV8/5TS2373b\nrLONjcXvD0leH0H+J0FLYiVVr7Q3EUbAXQ58ND1dnmdyJEx9PfzHf9jrK69MLuA7bNFJCBcHl899\nCqW5ULPHK5IJlE7CjdrRYTdokeJ9DrMpp6F9PkupZwXcsiV8S7K46ckxYMXi36DwDyLYsp74gxil\nBS7KayioC7WcxvZ+K1+xNlpJCqag/xN/Saw+fWxZ377Fk9sc5RFYwKnqb1T11kJTnAN15GfwYPvS\nb9+eXMB3WBeqf9sgQiSIgAtjgcslOL2bUhICbvt2m3sCOyjLl8P8+fb6iivCCfM9e0zk1td3d0N7\nLclUo7dA+rNHzzzztJxjLpRh2r9/sOPUWgzY6tXWeHzQIDj++MLbZteI9BfwbmyEo46Kf7xJE6WA\nizJOLKiAe+WVzLU7eXK472rYB2L/9eGVdGpqil4whfmfeCWxvvc9e/+xjxVPbnOUR+hODOn4twtF\n5BPp+dg4BuYIxvLl8P735zbZxxnwHdaFCuEscIVumqW4UHPFgnkWuCTi4EopIeJlYvqz2sIIc7/r\nJ5dojMON2j17VLqNuVCG6ZQp5k4qRi3GgHnWtzPOKN7jGLoX8N6xw8r37NwJV10V71grQZQu1Cjj\nxILEwHnX9OrVmWVhvqtB4+z8eNfHl79s76+6KlrB1N5uCXIisP/+wT83frzN16yJZhyO/IQp5Fsv\nIj8DVgF/BH6Znq8SkZ+KiGvLVQEqFfBdigUuKhfq4MEmSLZvD564UWkLXNgSIv4suo6OruuCCvN8\nCQweUWeiBskeveACuPDC/Nvs3RuskG0txoAFcZ8W4/rrzTV1++3lN0+vJnbutOu1sRHGjSt/f1HG\niRWzwPmv++xwhKDf1VJCUjwmT7b5smXhP1uINWvs7xk3zq65oHgCbu3aaMfj6E4Y0XUtFuf2NWAC\n0JSefy29/Jpoh+YIQiUCvnfvNkFiyQDBPxeVgKurC289ynWDTNICFzYDNQphXkzARZ2JGmTMe/YU\nt7DV15sLqCcFRXd2wsMP2+tyBNyBB8JXvmKvP/e57uK+0pRafNl7iNp//9x9YsMSZZxYsSSGKL6r\n1SjgSrWI7refzZ0FLn7CCLiPAP+hqt9X1dWquic9/z7wDeCyWEboKEglAr79T6Rh4rmiioGD8G7U\nXGImSQtcWBdqFMI8qAUuKhdqkDGrFs/Q6+iw3pX+GDCPj32sNoOiFyywMjYHHGDB7uVw9dVm5Xj2\nWXPRVQvlFF+Osgachz9ObOBAWyYSPk6smAUuiu9qNQq4UmMSW1rs4X7jxtz9Wh3REUbAjcJKieRi\nUXq9I2EqUfSzFPcpRGeBg/CZqMUscGHT/sMS1oUahTAv9qMQtQs1yoeEtrauMWBj05G2V19dW5Y3\nD698yFlnFc8yLEZzs1l9AL7+9eqo5Vdu8eUoExj8+K+hfv3se/5f/xX8Gtq5067FPn3ibSVVjoAb\nM8auiY0bM/eZKCj1f1JXl3GDr1sX3Xgc3Qkj4F4CPpBn3QeApeUPxxGWShT9LCWBAeIRcGEtcP4x\nDxtmT+atrfHXQwvrQo1CmCftQo3yISF7X14QtT9IvJaIIv7Nz0UXWTLEpk1w2mmFM36ToFw3YtRN\n7LMRMesnhLO4+61v+YR3FN/VcgScSDxWuHJEtUtkSIYwAu7bwGUi8pCIfEpE/l1EPikiDwGXptcX\nRETGi8gcEXlBRJ4Xkc+nlw8TkQdF5OX0PKedIt0F4uX0dGmIsfdYKlH0s5oscEEFXK4x+2vBxR0H\nF1bARSHMk05iCDJmkeIWqFx/Vy3/IOzcCY89Zn/3294WzT5FrIg3wOLF+TN+k6JcN2JcFjg/3r7D\nfNeDFPGN4rtajoADJ+B6K2HqwN0FnAP0B34E3AP8GGgGzlHVPwbYzT5gpqpOAU4ErhCRKcDVwMOq\nehDwcPp9F0RkGPAt4ATgeOBb+YReb6ISVbBLtcANG2axEVu3Fg9kDxoDF0R8tLeb0BOxTgx+koqD\nC9uFIQphnnQMXJAx9+1rrqxC5Pq7atkC989/WnbtMcd0r8dXKsuXw5e+lHtdJfrFlutG9CxwSQi4\nUi1w+Yjiu1qNAq4cq6iXyOAyUeMlVOkPVX1AVU/CMlBHA02qerKqPhjw8+tV9Zn061ZgCTAOeDfg\nFQK+FXhPjo+/HXhQVTer6hbgQUxQ9npyBesCfOIT8QR8l2qBq6sLlsjQ2ZmxrGULLo8wFrjsNlp+\nqtUCF4UwT9qF6h9zdiahN+Y//QnuuSf831XLAi5q9ylUX7/YctyIqvEkMWRTjgWukIAr9F2try/+\nXd271x6i6upKF/hRC7i2Nrtv9u2b8ZyEwVngkqGk2m2q2qmqG1S15CY8IjIBOBr4F9Ciqp5j7TUg\n13PIOKwHq8fa9DIHmWDd7dszN5urroon4LvcgFso7EbdvNlE3JAh+Z9swwi4QoIzKQtcKY3syxXm\nSbtQITPmE0/0liiDBnXN/MvVZSB7m2x6goAr1P80LNXWL7YcN+LmzeYCHjgwc03GQSkPa0EL7GZf\n016YwNSpxb+rnkgcObL0EipRCzjvfnjAAeEqDXg4AZcMBeuBi8j3gB+r6tr060KoqgaqDy4iAzAX\n7BdUdbv4gmJUVUWkrJxAEZkBzABoaWkhlUqVs7vEaGtri2Sso0dPY8OGIdx110KOPTb66PylS6cB\nQ1i/fgGpVLi0p8bGw4ERPPTQYvbs2Zhzm1WrmoHjGTBgJ6nU3JzbrF8/EpjKiy++QSr1fMFjzp07\nDDiSPn02k0pZIrV3rtvahgNHMG/eJlKp50L9LWFYufJoYDArVjxLKhWud9VFF9l0wQUns2VLH049\n9SnWrNld8Oa4a1c9O3a8hT59Opg//585486WL+8PHMfatW2kUvNCjakYo0ZNBvbj8suXcMkl9gu1\nZk3XG7r3d/nJ3sZjw4YBwLEsWRL9WONk8+Y+LFp0Mv36ddDe/hipVDTpzm1tpwHF01lbW5VU6pFI\njlmIU07pxy23HEd7e34FUl/fwUknPU0q1TV+4sUXBwLTGTWqjUceie9/u3mzHWfx4uDX0DPPTALG\n09q6nFTKLsxC92nvmp43byhf/vJRdHRsY82aZwt+V5cutWu7f//Sr+033ugLnMQLL+wllXqipH34\neeIJuy8OHpy5Z4bh9dftXL/4Ynnf16h+E3ssqpp3AlYAR6Vfr0y/zze9Umhfvn02An8HvuhbthQY\nk349Blia43MfBH7pe/9L4IPFjjd9+nStFebMmRPJfj7+cau29ZOfRLK7bhx8sO3/hRfCf3bGDPvs\nT3+af5tHHrFtTj45/zYPPWTbnHFG8WPecott++EPZ5Z553rBAls3ZUqg4ZfMlCl2nOeeK30fZ59t\n+7j33uLbLltm206YkH+b1attm7FjSx9TPt75Ttv3NdeU8Qf7eOMN29/gwZHsLjF++1sb9znnRLvf\ngQO9inqFp0GDoj1uIWbNUm1uzj2O5mZbn4s//MG2ec974h3fxo12nIEDVTs7g33mQx+yz9x2W2ZZ\nkPv05s32ub59VffuLbztfffZtmedFWxMuejosGOB6vbtpe/H40c/sn196lOlff611+zzw4aVN46o\nfhNrDWCeBtBTBY2jqjpRVRemX09Iv883FY1eEDO13QwsUdUf+Fb9FctkJT3/S46P/x04W0SGppMX\nzk4vc2RxyCE2XxpTYZdSkxggmAu1WAIDROdC9dwqK1fGWwuuFBdqNl4D84ULi29bzH0K8bhQPTwX\nzJgxARqbBmD4cEt+2LbNwgRqhTji36Ay5YOKce658OSTmfd+q++f/5zfjZhEBirY9T5ggLlrg17z\nQRvZZzN0KBx8sHUeea6IYb/cBAYwN6cXLhNF4kq5ZV1GjrTaeZs3W0KNIx7C9EL9iIjkDLFMlwH5\nSIDdnAJcApwpIgvS03nAd4GzRORl4N/S7xGRY0XkJgBV3QxcBzydnv4zvcyRRZwCbtcu+wFtbAzX\nRssjKgEXphNDoRvk4MH2d+zcmTluHJTSzD6badNsvmBB8W2DCLjmZrvJ7t4dbcV0f1B6VALO31C7\nVuJqVOMTcJUoHxSE1labH320xbFefrm9nzMn/2firgHnIRI+5rVUAQdw/PE2n5s7CqTbMcoRcBBt\nHFy5otpfzNdlosZHmPDEW4B8IfET0+sLoqqPqaqo6pGqOi09zVLVTar6NlU9SFX/zRNmqjpPVT/u\n+/yvVXVyeip6vN7KoYfaPA4B5xdDpVSU9wRcoSzUMBa4IE/SxcRMKdlpYdizxwRSQwP071/6fqK2\nwIlkRHiUhYw3boQdOyyYe8CAfZHtt1YSGbx+oAMH2oOKCPz859GW9KhE+aAgPPOMzY8+2uaXXWbz\n227L37c1KQuc/xhBv+tBkxhyEVTARWGBg+oScOASGZIgjIAr9HM9HKghx0bPZuJEu4mvXh29+brc\nm40nKApZ4II89TY3W4r7rl3FrUfFxux3o8bBtnTOwpAh5bVROuQQ+5tXrCjuRgwi4CAeN6p3HidO\nLL9tlJ9aEHD+fqA7dtgy1XiK6yZdPigIzz5r82OOsfmpp5plbd06ePjh3J9JogacRxgB19kZ7GEy\nH7Uq4PwWdCfgqpuCAk5E3i0ivxaRX6cXfcN775t+j8W1PR37aB2BaGjIPHm//HK0+y61BpxHVC5U\nkeBu1GI3yLgtcFHEv4H9Xw8/3F4vKpIYFvRHIepivhCfRaXaBVy5/UBLwd/rc8iQvQB85SuV6xfr\nWeA8ASeSscL95jfdt+/oyPw/vQepOAlTSsQrZzR0qIUahOWoo+xB+oUXMq7lXFSbgNu0yerADRpU\nWpiMhyvmGz/FLHCjgCPSE5gL9Yis6QDgAeCTMY3RUQJeHNyLL0a733ISGPyfe/31/C6VoE+9Qd2o\nxaxRcVvgwnZhKITnRi0WBxfUAhd1MV/I/DhG/YNc7QKuksV1RWDSJGtzEMTFHge7d8Pzz1v805FH\nZpZ7iRT33tu92fq6dXZORo82q3rchImBKyf+DSzp5qijzKI1f37+7apNwPljEsuxoDsLXPwUy0L9\nlaoep6rHAY8AF3rvfdMpqvoxVY25lr0jDHElMpRrgevTxzoidHZarFQuwgq4QhY4r41WXV3+rg61\nYoGD4HFw1eJCjZJq/0GodHHdyZNNwAVJcomDxYth3z679/hjPSdMgDPOMIF3111dP5NUAoNHmO96\nOfFvHkHcqFEJuPHjzeK3bl15oTNRWdCr/fvaEwjTC/UMVV0S52Ac0RGXgCvXAgfF4+CCCrggLlRv\nXyNG5K9yHnc7rVoQcM6FWj7l9gMtF88CVykBlx3/5sdzo956a9flSSYwQLiyQeVa4KC4gNu3zx5k\nRUqLs/PT0JA5j54wLoWo/ifOhRo/YcqI/FpE7syz7g4R+VV0w3KUS9wWuHIEXKE4ONWMZS4KF2oQ\nIePd1FetMstg1ERRQsTDE3DPPWc3/1yoBhfateRC9Z7o167N736vJOX0A42CSlvgsuPf/Fx4of3d\nTzwBL72UWZ5kAgNYXNewYWYN9O5l+YiivEcxAbdxo31fhw/v3qe5FKJwozoLXO0QJgv1LKz9VS7u\nwZrN906uucYeoYJMM2Z0//yMGSDC6WecUfzz11zT/fPnn99tu0NONX/h0vmtqH/djTd2//z06YHH\n//oSM3d1EURjxwb/++fP7y7gfOu31g1l3z4YyHb69svx+VdfffOwb7pQP/nV/OOdbql4LYseyB3Q\nMX8+/QcII9nA3r2wvn5c/rGPHdv98//3f0X/5q2fvhqAoX/9TffP33hj8HN3/vkMGWL9CXfvTieo\n5Lj2ttQNo70dBrOVpubC196wv98BwObv/CySa69T6lj1ktV+m3jkgK7XdJnXXtND/8fIkeaGfPPH\nN+S1142gn8269gB771t/cetPqaNw2ZQuxXXnzw9+7ADX3iWXn0xfdrNiBWyTwV0/P31698+HvPa6\nkXXtPfOLfwFwzMzTu32+/5UzeO977WNvWuFmzGDFt28H4MBvf7Tsa6/g5Lv23nSjnnZZwc9s+P+u\nA2DUz75l5zqbANfeIVPqGMh21qzJ8cAqwutj7ImsZePisq49b5o860cAvPzvX+66LpsC196KGx+w\n8/S5dwS+9nJNI0YJfdnN1q05rM4Br73Tzzgj0LVXcCrwmxtoynXtVQlhBNxIIN9z+hYs4cFRJYxg\nE8PYRBsDWc+YyPb72pa+QDQWuFy14N7AzG4jKV5V900XKjnrS9sxMKXZQuHH7YnYY+dKJhQ9bli2\nYqa3IfXR+M6KuVFfx/45xf5mgGF9rdbFFiLIsMDO9x76MYI3GMCOSPbpp5rdqOdwP50U7kYeZ3Hd\nBjo4nMUALOLIIltHyz7q3zzmNHKbAHPVhFuBqSnv+5cEbwq4veMKbrch/ZM2ig0lH6sO5bh0gYan\nc9RpCPNdDcJkzPS2jMkl7+MVLCDxQMrwwwIC7If5T50bNR7CCLhVwFvzrHsr4P5FVcYhmP90KYdE\nts/Xt5qAKzWJwf/ZXC7UMALuTRcqw/Ju490gR1OgcjAwgZVA5gclSjICrkAtgRAUE3CeaC32NwMM\n7WvRzoXOYRi88+edz6ipVgHXygBm8gNAaKCdRvZ2Wd/I3kSK63riaQHT4jtIDl7kUHbTxIEsZwjb\ncm7j1YRbuxb+8Q9b5omFJAXchAk2X7m38IOtd+8oR8ABbwq4XG7UahNwHdSxGvuSRfEdHo/5T50b\nNSaCNEy13qp8FdgNXAEMSC8bAHwG2AVcHXRfSU69sZm9x0c/ag2Ff/7zaPa3Y4ftr0+f4M2gc3Hn\nnbafCy/svu7ee23dO99ZfD/etu96V/5tvvAF2+b73++6PPtcX3WVbXfddcWPG5b3vc/2fccd0ezv\nnnsKN0j//e9t/fveV3xfTz1l2x57bDRju/12299732vvo76mP/952////m+kuy2Lzk7VD37QxnXk\nkaqLF6tecYU1kq+rs/kVV6guWxbvOObMmaM//rGN4/LL4z1WNrfease96KLC211zjW33oQ+p7txp\nrxsaVPftS2acqqo//akd9+MfL7zdSSfZdv/8Z9flYa9p7/t69tnd133/+7bu858Ptcu8vPSS7W//\n/Uv7/KpV9vnRo6MZzyWX2P5uvrm0z7tm9mU0s8/if4DbgZ8A20RkO7ANuAG4Nb3eUUVEnchQbhst\nj0JJDGEqnwfJQg0azO89lceRiRplFioEsMAFzECF6LNQ484q9AKjq8kCd/PNcMcdVjrjrrtg6tRM\ncd2ODpvfcEMyxXW9frlJ14IrlMDg5yPpjtn33psZ4wEH5M8Qj4OgpUSiyEKFrokM2ZmvUZUQ8Zgw\nwc7lmjUWJxuWqL+/LhM1XsKUEelU60t6GPBZTLBdARyqqp9Kq0ZHFRGXgCvHfQpFYuBCCLggWahB\nxxy2yXUYohZwEydaRt/69ZkfGT9hBFzUWahxZaB6VNqF6vU5HTTIagsOGACf+pSt+8UvMt+5SuEV\n0F28uHhNuijJ7oGaj4kT4YQTrP3dW95iy1autHMaZYeKQgR9WItKwI0bZ/e8rVu7Z4dGLeAaG+3v\n87fDCkPUAs5losZLGAscAKq6VFV/rqrfUdVfqOpLxT/lqARRd2OIogYcdI2By5b9pQi4Qha4oDfI\nOC1wUXZiABMOhaxwYQScJyq3bo2mhEpcRXw9King/H1OW1vt2t2xw6xsDQ2Z67GSDB5scWZ79kRf\nQigfnZ2Z0iXFBNzs2Zl6cV4ZnI6OeHrF5sP7rq9enb8cza5d9j9ubLRzWg4i+cuJRC3goLxSIlEX\nVnYCLl7C1IE7r9gU50Ad4Zk0yczpK1eWZk7PJioL3MCB5m7atat7U/ZSXKibN+cvyhlUzBxwgM3X\nrMlfX61UorbAQWEBF+ZHoaHBfqBUzdVXLnG7UCsl4Ar1OQW7ZqLuc1oqQdutRcXy5SZ2xo0rfM15\n53Dv3u7r4uoVm4umJrsf7NtnXQty4be+lRMu4lErAs65UGuLMBa4vwH/l577p//zTY4qok8f+yKq\nlt8fD6KzwEH+OLgwAq5PH3Nh7duXu1l0e7uJu7q64taRfv1sTIVu6qWgmhFw5T7J+4nKAgfRuVH3\n7csIK08QR01Li1lFNm4sr11QWCrZ5zQsScfBBY1/q6ZzWMziHkURXz+9VcA5C1y8hBFwE4ED03Nv\nOgb4GvAycErko3OUTZRxcFHebPLFwYWNOynkRvX2NXJksCDpOOLgPItNv342RUWUAi6qfqjr1plL\nasyYaP9WP3V1lflRqHSf0zB4Ai4pC1zQ+LdqOofFvutRxb95HHuszZ99NmOB7OzMPLBGdRyoLgE3\nbJhZPLdv7+5tcZRPmCSGVTmmBar6P8BNmJBzVBlRCriwwqAQ+WrBhbHAQeFM1LDjjSMOzrO+RRX/\n5nHEESZmliyxeCePjg47hyLhz2G5mahJ9bWshICrdJ/TMPgFXBKpZYV6oPqppnNYLBM1ikb2foYM\nsXvxnj3WBg/sntXRYev69o3mOFC6gNu92xo81NdnXJ/lIuLcqHESOokhD88CZ0a0L0eEVLsFzi/g\nVMMLuEKZqGHHG4cFLo74N4DmZjjoIHNbvvBCZvkbb9iT/YgR5moMQlQuVO+8xZWB6lGJOLhK9zkN\nw/jxdr1t3Ni9A1PUqAZ3oVbTOSwm4KK2wEF3N2oc7lOwv03Evo+54g3z4X1/Dzggmr6sHmEfuPyZ\n3meeeRqDBiWbpVxLlC3gRKQPcBmQo6qXo9LEIeCisMDlEnCtrXbDaW62KQiFXKhhb5BxWuCiFnCQ\n241aipU0KhdqUha4Sgi4iy8uLoi79DmtICLJxcGtWWPfvREjilttqukcvtmNYWXu9VHHwEFyAq5v\nX/uOdHbCqlXBPxfX99cTcEEscN0zvYXW1mSzlGuJMFmoT4vI3KxpAbAB+BBwXYB9/FpENojIYt+y\nP4jIgvS0Mr3PXJ9dKSLPpbebF3TcvZ1DD7X50qXlu1OiTGLwBIY/Bi6s9Q2idaHGYYGLuoSIn1yx\nTqX8KNSaC7USAm7mzGDiI64+p2FJKg7OH/9WLFuzms5hT7bAQWlu1Li+v56wL2aBK5TpnWSWci0R\nxgL3fI7pSeD7wJGqeluAffwGOMe/QFXfr6rTVHUacA/wpwKfPyO97bEhxt2rGTXKsh+3bs0IpFJo\na7OaV337mmm7XHJZ4EoRcFG6UHurBc65UIszaZL1Mc2VnNHYSCJ9TsOQlIALGv8GmXPY3NxdyCV9\nDsePtxjStWtzuxnjEHBHHWV/55IlFtDfWwRcUBdqNWUp1wphkhguU9WPZk2fThf0fT7gPh4Fcv5M\niIgA7wPuCDomR3FEoino63efRlEXKWoBV8gCF/QGuf/+dlNfty5c7EghkhJwnnXVuVDj49xz4X/S\nDQMbGuxaGTQIZsyARYtsfbWQVC24oPFvHueea+dqxoxMN4tKnMM+faxunWpuYRF1EgPYw++0aXbM\n+fOrR8B5MWf/7//Z+29/O9qYs6Au1GrKUq4VokpiiIK3AK+r6st51ivwgIjMF5EZCY6r5okiDi7q\nm01UAq6QCzVszF5jo5n7Ozujy3CM04U6dqwJ2C1bMjfHSgm4PXtM+PrLfMSF/4k+6QZ+3nX25S8n\n3+c0DFOm2PW8bFm8WZ1hBRzYuapUr1g/hdyocVjgoKsbtRoEnD/mzCtgvmtXtDFnQV2o1ZSlXCsU\nzDURkX+E2ZmqlpOJ+kEKW99OVdV1IjIKeFBEXkxb9LqRFngzAFpaWkilUmUMKzna2tpiGWufPvsD\nB/LQQ2s46KDSHqv++c8RwOE0NGwklVpcdPtidHZCff1b2bKljgceeIQ+fZR//Ws8MIndu9eQSgUb\n57p1w4AjWbZsE6nUc13WrVhxHNCf1aufJpXa0WVdvnM9ZMg0Vq8ewp//vIDp07eW9sf5eO65ScB4\nNm1aTioVfd2LAw44ik2bhvLb3z7HySdvYtGiw4AWNm9+gVQqR6PUHKxaNRg4mpUrt5JKlWayWbeu\nCdUTGDVqN48//tSby+O6pgcMOIW2tkb+8pfHGTIkuaafc+ZMBUYiEvz8JkX2ud5//2NZvnwAt976\nDFOnRl+Ea/PmRl599RSam/exevVjNVcmoqnpUGA099+/lIaGzJNkZyds2HAaICxZ8gjLlnV9Sijn\nmh44sAU4jPvue4O9e+uA4WzY8BypVIF+gCWwZUt/4DgWLdpJKjU35zbr1vXj4x8/jt27uxfJbG+3\n6YILOrjppqcZN670Vj6trQ3AqaxcuY85cx7L68FpajqVnTuLp7/267ePVOqxksfTo1DVvBPwx6xp\nLdAOPAX8NT3fC6wB7iq0L98+JwCLs5Y1AK8D+wXcxzXAl4JsO336dK0V5syZE8t+//hHVVB95ztL\n38fPfmb7+MQnohvXuLvSiiQAACAASURBVHG2z5Ur7f3Mmfb+u98Nvo8nn7TPHH9893VDh9q611/v\nvi7fub70UvvMr34VfAyFuPzyaPeXzRe/aPu/7jp7f8YZ9v6hh4LvY+FC+8zUqaWP44EHbB+nndZ1\neVzX9JFH2vHmzYtl93k55BA77oIFyR43CNnn2ruWf/azeI43e7bt/61vjWf/cXPNNTb+r3616/KN\nG235kCG5P1fONb1kie17/HjVY46x1089VfLu8rJjh+27oUG1vT33Np/+tGpjo22Xb2psVL3iivLG\n0tmp2r+/7W/r1vzbJTWeWgCYpwH0TUEXqqq+15uA+7H4tUmqeqKqvktVTwQmA1uAB8vQkf8GvKiq\nOZ/hRKS/iAz0XgNnA+WbgXoJ1ehChe5u1ChdqHv3mmuxvj5ck/Fi5QXC4rlQ44iBg+6JDKVkCkfh\nQk0q/s2jEnFwu3fDyy/bNeV9p6qZuOPgSnGfVhP5vutxxL95HHywxfytWZOJSY7DhdrcbDF+/vZ2\n2SQVc+Yv5lvIjVpNWcq1QpgYuK8D31TVLpdD+v01BOjEICJ3YJmrh4jIWhH5WHrVB8hyn4rIWBGZ\nlX7bAjwmIguBucB9qnp/iLH3aiZPti/RK6+UHpwfZRcGjygEXL4s1LBttDyKlRcIS1ydGDyyf6TL\niYErp4xIUhmoHpUQcC++aO61yZPjaxUWJXHXgqt1AZfvux5X/BtYjKjXVsvr5RuHgIPicXBJxpwF\nyUQtlOkN1ZfpXQ2EEXCjgXwNP/oARS93Vf2gqo5R1UZV3U9Vb04vv0xVf5G17auqel769SuqelR6\nmqqq3wkx7l5PU5NV1+7oMBFXCnFY4LJrwZUi4IYMMXG6dav9fR6l1qyL2gIXZxYqwGGH2VPp8uVm\nhdyyxTIkPVEWhKYmy8rbvdsCmEuhN1jgnk/n2h9+eHLHLAdP3C9a1PW7ERVBe6BWK5UQcGAdVPy0\ntMTTaaCYgEuyM0bQTNRzz4UrrrDXjY0gom/GzN1yS3VlelcDYQRcCvgfEelSg01EjgP+B3gkwnE5\nIsZf0LcUouzC4BGFBa6+3sSRalcLUqnjjcsCF5eA69PHMg5V4aGHbFlLiz3pB0WkfDdqpQRckv1Q\nF6eDNqZOTe6Y5TBsmJ2nXbvM9RslW7bY/7xfv8y9pdYYO9ZEwuuvd31wiaMLg8fs2fCb33RdFlen\ngWICLsnOGEEzUSHzoHTrrfCPfzzCV75i7x8sJ0irhxJGwM3AYuD+JSKvpjsivIolMmxOr3dUKeXG\nwUXZhcEjCgEHud2opVoMx40zC9b69WaRKhWvtpInbKZNi6+fn2dp+fvfbV6KyC7XjZq0C9V7oncW\nuMLEFQfn7e+oo6Ltm5kk9fWZBwG/xT0uC5zXaWDPnu7r4ug0UEzAzZxZ/H8XVcxZ0GK++/bB44/b\n67e8xeaXXmrzu+7KuJ0dRphCvmtV9RjgfOCXWCzbL4HzVfXofAkIjuqgHAGnGr8FbscO+3L27QsD\nB4bbT65ivqXG7K1cmenD2txMSY2U/bWVPNra4uvn58U6lSPgyunGsHOnXR+NjWbVSIJKuFA9C1wt\nCbi44uBqPf7NI5fFPa4khqQ7DRQTcJMmwXHH2evs0h5Rd8YI6kJduNAskgcemLHaHXYYnHCCda/4\n85/LH0tPInQhX1WdparXqnVhuFZVZxX/lKPSlNONoa3NfqSbmqKJh/Dwx8D5rW9hOz3kykQtxQLn\nCa/WVnuvGt69UYl+fp6V5dVXbV6OBa4UAedZLw44IFzCSDmMHWtu4vXrc1s0ombHDvuRb2zM/DDW\nAnG11Kr1+DePXP2P47LAJd1pwLtOly/PHQP53HPwz39m3KRxdsYI6kJ9NF3Z9a1v7brcs8Jlu597\nO6EEnIg0iMj7ReQnIvK79Px9IlKjRvTeQzkWOL8YiqKNloffAleq+xSicaH6hVd2df8wwqsS/fw8\nAedRipu7HBdq0u5TMNfPuHH2et26+I/3wgs2P/TQ4nFD1URcLtQwPVCrmVz9j+OKgUu608CAAfYw\nt3dv7u/It75l97pPfcrizeLsjBG0e4on4E47revyD3zA4n0feijZuNdqJ7CAS3dAmIeV+3gHcGB6\nfifwtIiU8NPrSIqxY+0LvWlT7rZThYjDferf3+uvZ45RjoArx4UalfCqRD+/rVuhf//M++uvD+/2\nLceFmnQCg0eSbtRaS2DwmDjRQhJeey3zHSuXHTvMkt/QUFvu5FzkcqHGZYFLMuvTI58bdf58uPde\nS0L56lejO14+Bg+263DnzkxiVzadnWYRhO4WuKFD4T3vMfHneqFmCGOB+wEwHDhRVQ9U1ZNU9UDg\nhPTyH8QxQEc0iFgRSQhvhYsjgQHsiWr4cHvqW7LElpUi4KJwoUYlvJJ+yvbcvv7g3j17wsfbleNC\n7Q0CrhYTGMBcYtnFnkvFS8wZNcp+SDs7LcA9jsScpEgyBi7JrE+PfALum9+0+Wc/m/GExE0xN+qS\nJXYPHzcu973kssts/pvfJN8DuVoJI+DOA65S1S6N1VT1aeCrmDXOUcWU6kaNywLn3+dz6TamlXKh\nRiW8knzKjsrtC7XnQoXgmW1RUKsWOIgmDs6fmOM9LHR2xpeYkxTZdR937bK414aG6Ev/VKLTQC4B\n9+STMGuW3YO8Eh1JUOz76o9/yxWqc9ZZJjZffhmeeqr7+t5IGAHXF2jNs64VK+brqGJKFXBxWeAg\n8/S3aJHNo3Ch7tkTvo1WVMIryafsKOPtnAu1MLVqgYPy4+AqkZiTFC0tlpy1ebNlOXqxuKNGRRvv\nC5lOA83N3e8RUWd9euQScN/4hs2/8IXS7relUiwTNV8Cg0dDg91fwSUzeIQRcE8BV6V7kb5J+v1V\n6fWOKqZcC1ycAs4LEo/CheqPYQla0DYq4ZXkU3aU8XbOhZqfrVvtR6epKfm/MQrKtcBVIjEnKUS6\nJjLEWcQXLKtz0SLL8owz69MjW8DNmQMPP2wxaV/8YrTHKkYhF6pqcQEHmWzUO+8svWtMTyKMgJsJ\nTAXWiMidIvKjdG/TNcCU9HpHFVNqN4Y4+qB6eALO+4GIwoVaisUwKuHlPWXnKpAZ9VN2lPF2pbpQ\nt22zzzQ1xdd6KB9JCTjP+nbYYcmVSYmSpiabL1mSEQxhklwqkZiTJP5SInG30QL77t9wQ7xZn/5j\ngQk41Yz17Utfiq8/cz4KuVCXL7cySCNG2PcsH1OnWu06VxPOCFPIdwFwEHAjMBI4C+t/+gvgIFWN\nqWWyIyq8HnzLllnF66DEaYHLFoVRuFBLidkr5N5oaAgnvM45x25EYNmhcT1lRxlvV6oL1R//FrXL\nqRh+ARdnUHMtu09nz4bjj8+8L6W2YdKJOUnjt8DFlcBQKTZtsuLou3bZfejxx+39+ecnP5ZCLlTP\n+vaWtxS/j/iTGXo7gQSciDSKyClAH1W9WlXfpqpT0vOvqerGmMfpiID+/e1L1N4ertdnnEkM2RlQ\nUbhQSxWc2e4Nj7e+NZzwWrLErIAtLfakGNdTdpTxdqW6UD0BVwnX4pAhJk7b2vKXJoiCWk1g8Meu\nZRMmdq0S5S+SxJ+JmoQFLim8xJPsQtft7XDyycknnhRyoQZxn3p4NeEefLB4Z4eeTlALXAfwD6BG\n2xY7PMLGwakmk8TgUYqAGzjQrGQ7dtjNqpzx+t0bP/2pLRs2LJzwuv9+m599drim8mGJMt7Oy7jz\n3DpB8R4Eks5ABXtSTyITtVYtcFHFrlWi/EWS5HKhxhUDlxSFxHtnZ2UST/wWuGyLeRgBN2wYnHmm\n7WPy5NLCAnoKgX5eVLUTeBmIwQbjSJKwAq611Zq6NzfH84TtF3Clpu6LdI2Di8pi6FncHnig+A+h\nH68n6dvfXt7xixFlVlt9vQU2q5qIC0qlEhg8koiDq8UeqBBd7Folyl8kSa4khlq3wFVj4snAgXaP\n2bWrq6V/zRo794MGde8qk4vZsy0ZA+yBvZSwgJ5CGPvA14FvisgRcQ3GES/Ll2eKeX7pS8GeWuJM\nYMje74gRpcdR+d2oUcXsTZxoAbXbt8MTTwT7zK5dmafJs84q7/hBiDKrrRQ3aiVdqBC/gHvjDftR\nHzgwY0GoFaKKXfM/KGQTV/mLJPG7UHtKDFy1Jp7kcqN63RdOPbV4kpBnWczV/7jWS9qUQhgB9x9Y\nx4UFIrJaRJ4Wkbn+KaYxOiLAi4d48snMsiBPLXEmMCxfDldfnXm/YUPpZnC/BS5Kl+870uWp77sv\n2PaPPGIWy+nTk/sRiCqrrZRM1Eq6UCF+Aee5T6dOTT5Jo1yijF0791y47TZ7XVcXf/mLJBk61P6W\ntrZMR5haF3DVmniSK5EhjPu0Gi2LlSSMgHse+BtwG/AwsDi9zD85qhB/PER2fFOxp5a4Ehj8ld09\nyqns7s9EjXLM551n81mzgm2flPs0DsJmoqr2fBdqrSYwQPSxa9736pJL4i9/kST+WnCesKh1AVet\niSe5YlbDCLhqtSxWijBlRC5T1Y8WmuIcqKN0ynlqiSOBIY7K7nG4UAFOOcXcZ88/D6tWFd++lgVc\nWBfq5s32BD9oUPI1pTySssDVWvwbRB+7Nm+ezY89trxxVSPZDyC1LuCqNfEk24W6YYNZPZuazGtR\njGq1LFaKogJORJpE5EIRmSkiHxKRkn8WReTXIrJBRBb7ll0jIutEZEF6Oi/PZ88RkaUiskxErs61\njSM35Ty1xOFCjcMM7lngXn3VSko0NGQESTn06ZOJZStmhVu92m5GAwfCSSeVf+ykCetC9btPK+Ve\n9ARcXFmotWyBi7p1kyfggvzQ1hp+ATd4sNVKq2WqNfEk24X62GM2P+kku9cWo1oti5WioIATkQMx\n1+gfge8DtwNLReTsEo/3G+CcHMt/qKrT0lO3n0kRqQd+CpyLdX34oIhMKXEMvY5ynlriSGKIwwzu\nCbgXX7R5mDZaxfDi4IoJOM/69ra3Fb95ViNhXaiVdp8CjBtn83XrwhWnDoJq7WageuSrbfjhD4eL\nXdu509rd1dcHyxSsNfzXcK1b36AyfVeDkO1CDeM+heq1LFaKYj9x3wM6gbcAzVgrrWeBX5ZyMFV9\nFCih2yLHA8tU9RVV3QvcCby7lDH0Rsp5aonDAheHGdyzHnkuryjHe076kePhhy1BIR+17D6F8C5U\nfxeGStG3rz1cdHTA+vXR7nv9erPmDhsWXxZ2EviTXN72Nlt2/vnhfrwXLrRzPHVq7mzUWmb58kzt\nRoBXXukZNcWS7rsahGwXalgBV62WxUpRTMCdBPyHqj6uqrtVdQnwSWB/ERlT5LNh+KyILEq7WHNF\n04zDeq56rE0vcwSgnKeWOJIY4jCDexY4r75dlOMdOxaOPtpKhKRSubfZtw8eeshe17qAC+tCrXSD\n97ji4Pzu01rLQM2H59r3Z6MHoae6T71kqgcfzCzr6Og5NcWS7LsaBL8LdetWWLDAfntOOCHY56vV\nslgpcrTc7sIY4JWsZcsBwYr6RvHM+3PgOkDT8+uBy8vZoYjMAGYAtLS0kMr3q1tltLW1xTLWU07p\nxy23HEd7e/4iO/X1HZx00tOkUl1NTKtWnQj0Y8WKp9izp4D5KQRnnHEQ9903ho6O/M8P9fWdnHHG\nq6RSywLtc82aIcC0N+sDqa4nlcpfrTjsuT788Ak8++wEbrxxLf36dR/T4sWD2LbtGMaP38mqVXMD\nJTxUG+vWjQAO56WXNpJKLS66/fz5RwDDaWt7jlRqU85t4rqm/TQ1TQFGcf/9L9DeviGy/f7lL/sB\nkxk6dB2p1MuR7TcugpzrAQOGAUdy//3beMc7ng287/vuOxQYzaBBL5FKvVrWOKuFdev68fGPH8fu\n3d3vi+3tNl1wQQc33fQ048Zl7n1JXNM9mYEDT6G1tZHvfncJqodx8MHbmDs397WY61w3NcGNN/bj\nj3/cjwcfHM2uXfU0NXVw1lmv8d73rqWpaXfeB+0eh6rmnTD36XFZy+rTy48u9NkC+5wALA6zDrME\n/t33/qvAV4Mcb/r06VorzJkzJ7Z9z5ql2tys2tioatE9mampydZn09mp2revbdPWFt1Yli2zsWSP\nwz81N9t2QVm4sOvnr7qq8PZhz/UTT9h+DzzQzks23/iGrf/c50LttqpIpexvOPXUYNsfeqhtv3Bh\n/m3ivKY9vvhFG8d3vxvtfi+/3PZ7ww3R7jcugpzrzZvtb+rbV3XPnuD7njrVPvfUU6WPr9r49Kdz\n3w/9U2Oj6hVXdP1cEtd0T+aII+zcnnWWza++Ov+2vfVcA/M0gL4JEub993Tm6AYR2UDG6vawf3l6\nXWiyXLH/jtWXy+Zp4CARmSgifYAPAH8t5Xi9lVzxEJ4J+hOfyB0PsW2bVbweMAD6949uLHGYwT0X\nqkfUMUvHH28uxldegZde6r6+1uPfIFwMnGrluzB4xO1CrdUEhlwMHQqHHmrf62cDGuB27LDs6oYG\ncyv2FFxNscrguVEfftjmQePfHN0pJuCuBX6EZYD6p3zLCyIidwBPAoeIyFoR+RjwPRF5TkQWAWcA\nV6a3HSsiswBUdR/wWeDvwBLgLlV1hYNDkh0P4WVV/vWvVkQ3mzi7MEQdYJst4KIec319JpkhOxt1\n0yZ4+mlLgz/99GiPmyReFmqQGLjXXrOEjuHDrWxKJYmjoX1np2VdQm2WEClE2Di4BQvsfBx+uLmv\negqupljyLF+eefDzfnPuuaf2E0YqRcEYOFW9NsqDqeoHcyy+Oc+2rwLn+d7PAgLWw3cE4cwzzXqx\ncqW1gDrjjK7r4+6D6gnKG24of1/9+pnlbudOex+H6HzHO+D3vzcB589yeughs0i95S3RWiqTxm+B\nU80duL98udXxu/VWe79li2XszZxZucDhOCxwq1fbD3dLi/Xo7UmcfDLccov19/3CF4pv31MTGAYM\nsHaCQbZzlM/s2VagPTuT/7bb4I47zOtSyy3ZKkFElbIctUhdHVx6qb2+5Zbu6+O0wMWBv3BvHKLz\n7W83UfPII12fyr0SBLXsPgWzrvTta+61Xbu6r/e3P/OEcjntz6Jg+XL4adr2v3ChWXGjKAFRyx0Y\nihHWAjd/vs17WgcGV1MsOfzdd7K9Pb2xCX1UOAHXy7nsMpvffTds3951Xa0JOL8bNY4xDx8OJ55o\nNxyvZIgqPPCAva51ASeS340aR/uzcvEE5e9+l1nW2hqNoKzlDgzFOOww6zawdm3XpuL56KkttFxN\nseRwTejjwQm4Xs6BB8Jpp5nF5a67uq6L24UaJcuXw8aNmfcTJ8ZTjDO7K8Pixda+a8wYOOKIaI9V\nCfIlMlTbDThuQdkTExg86ursQQSKW+FaW627SWNjz7i+/biaYsnhEkbiwQk4Bx/9qM1/85uuy2vF\nAudZYl71laeKyhKTzXnpqMxZs8z65s8+7QnFXvMJuGq7AcctKD0Xak+0wEHGjfrEE4W3W7DArvMj\njqj9/qC5qMZuBT0RlzASD07AObjwQgu+f/zxriUyasEC57fEWInADHG49qZNM2vbunV2g+8p8W8e\n+Vyo1XYDjlNQdnRY2Qzo+QKumAWupyYw+Km2bgU9EdeEPh6cgHMwYAC873322m+FqwULXNKuPRE4\n9VR7ffzxmVpGDzzQMwJw81ngqu0GHKegfOUVy5QbP95ixXoiJ5xg1/IzzxTu79tT498cyeISRuLB\nCTgHkHGj3nabPYVCPH1QoyZp197s2VY3D2Dv3q7j6Am9E/MJuGq7AccpKHtyAoPH4MH297W3Z7JM\nc9FTM1AdyeISRuLBCTgHYFalyZPNNfjgg+aOrAULXJKuPc9d6/Vb9dNTUuHzuVBnziz+2SRvwHEK\nyp5cQsRPMTfq9u2wdKkVqO7p58IRLy5hJB6cgHMA5k7xSorccgts3WoWpoEDq7v6epKuvWrLxIyD\nfBa4557L/O31Wb2/K3EDjuOJfvlyy1y+Nl2+/IYb4slkrhZOPtnm+QSc12rryCNNxDkc5eASRqLH\nCTjHm3zkIybk/vznTBB3NbtPIVnXXrVlYsbB/9/e/QdLWd13HH9/elFwAkYTlaaAoWCwIUyEkKKl\nmY6QYsASNGh+ODrVjilIOlPNkAmJ/aPajmHUmcbMmKQ1kRGTNqhVKkqwQUNKohAEhUCiEVBsxSCm\nQIMoKPjtH+ds7nK5d7mEvbv7PPt5zew8+5w9d+/Z89x57nfPz+4CuM2bOxd8njcPrrmm+TfgWt/o\n4dgDyupFig8eTGn79zd3keK+Vj0TtesEIPD4N6s/TxipLwdw9lvDhsGUKanl7bbbUlord59CY8dW\ntNpMzL7QtQt13z6YOTN1p11yCcyf3zo34O6+0VdaB7/yld4HlK24SHEjjBqVAvYdO+DFF498vR1m\noJoVmQM4O0xlnbP77kvH1atbuxupkWMrWm0mZr1t3ZpanCCNgzz5ZBg3Lg3qP/tsWLCg9da66/qN\n/tZbU/rR1jer1g5d492Rao+D8wQGs9bmAM5+a9kyuP76w9MOHmz9bqRGja1otZmY9VTpQnzwwc60\nvXtT9ymkTc9PPrk5ZTsWn/hEOi5dWnt5jGrt0DXek54W9N2zJ137/v3LPRvXrMgcwBlweDdSV0Xo\nRmrE2IqyToWvvvaV8V9dzZ3bute+2vDhqdVw377Uitgb7dA13pOeWuCeeiodzznn6H/zZtYcDuAM\naN9upGNR1qnwZbv2M2em4wMP9C5/2bvGa5kwIbVYr1+fgt4Kd5+atT4HcAa0dzfSsSjjVPiyXftK\nALdkSc8titXK3DV+NAMHpq7zQ4c6Jy2AJzCYFYEDOAPauxvpWJVtKnzZrv37358mXezaBStXHj1/\nWbvGe6u7blS3wJm1PgdwBrR3N1K7K9u1l46tG3XkSPjkJzt/tlqRu8Z7q+uCvrt3p/GOAwbA6NHN\nK5eZ1eYAzoD27kZqd2W89pUAbvFiePvt2nn374dHHknPP/7x8nSN91Z1C1xEZ+vb2LHQr1/zymVm\ntTU0gJO0QNJOSZuq0m6V9Kykn0laLOmUHn52m6SNktZLWttdHvvdtXs3Ujsr47UfPz4tTP3yy7Bm\nTe28CxemfX8/9KG0C0lZusZ7a8QIOP10ePXV1PLm7lOzYmh0C9xdwNQuacuBMRHxQeA54Ms1fn5S\nRIyNCN9a6qysMyzt6Mp47aXONeFqdaNWL/47b17rLVTcCF0X9PUEBrNiaGgAFxErgV1d0n4QEZW5\nYquBoY0sk3Uq4wxL650yXvvqcXDd7fUJcP/9qdVp5Mi0VVi7qh4H5z1QzYpB0dOdra9+oTQceDgi\nxnTz2kPAPRHx3W5eewHYDQTwLxFxR43fMQuYBTB48ODxixYtqk/h+9hrr73GwKKMFC8413VjNLOe\nDx2CSy+dyJ49J3LnnU8yYsS+w16PgNmzx7N58yA+//nnmDHj5aaUs16Op643bHgn1103jsGD9/PK\nKwMYMOAQDz/8Ezo6Gvv/oQh872icdq3rSZMmretVT2NENPQBDAc2dZP+d8BiclDZzetD8vEMYAPw\nZ735fePHj4+iWLFiRbOL0DZc143R7Hr+7GcjIOKGG458bfny9NoZZ0S8/nrjy1Zvx1PXGzdGSKk+\nIKKjI2LOnIgtW+pXvrJo9t90O2nXugbWRi/im5aYhSrpKmA6cHku/BEiYns+7iQFehMaVkAzK6Ra\ny4ncfHM6XnstnHRS48rUapYtg3PPPbyb+dCh1t8D2azdNT2AkzQV+CIwIyK62YkTJL1D0qDKc+AC\nYFN3ec3MKiZPhkGD0ji+LVs609etg0cfTWvbzZnTvPI1W9H3QDZrZ41eRuR7wCrgbEkvSboauB0Y\nBCzPS4T8c877B5K+n390MPATSRuANcDSiHikkWU3s+Lp3x+mT0/PFy/uTL/llnScPRtOPbXx5WoV\nZdsH16ydNHoW6mUR8Z6IOCEihkbEnRFxVkQMi7Q8yNiIuCbnfTkiLszPn4+Ic/LjAxFxUyPLbWbF\n1bUbdevWtCxK0da26wtl2wfXrJ14nW0zK7VRo6CjA1avTsuj9OuXdmeYOROGDGl26ZqrbPvgmrWT\npo+BMzPrK8uWpUVqK9tpRXS2OC1d6gH6ZdsH16ydOIAzs1KqHqDf3dz2N97wAP0y7oNr1i4cwJlZ\nKXmA/tGVcR9cs3bhAM7MSskD9I+ujPvgmrULB3BmVkoeoN87ZdwH16wdeBaqmZXSwIGwd2/v8rW7\nkSPh9tvTw8yKwS1wZlZKHqBvZmXmAM7MSskD9M2szBzAmVkpeYC+mZWZAzgzKy0P0DezsvIkBjMr\nNQ/QN7MycgucmZmZWcE4gDMzMzMrGAdwZmZmZgWj6G6X5xKR9CrwYrPL0UunAb9udiHahOu6MVzP\njeO6bgzXc+O0a12/NyJOP1qm0gdwRSJpbUR8uNnlaAeu68ZwPTeO67oxXM+N47quzV2oZmZmZgXj\nAM7MzMysYBzAtZY7ml2ANuK6bgzXc+O4rhvD9dw4rusaPAbOzMzMrGDcAmdmZmZWMA7gWoSkqZJ+\nKWmLpC81uzxlIWmBpJ2SNlWlvUvSckmb8/HUZpaxLCQNk7RC0i8k/VzStTnd9V1HkgZIWiNpQ67n\nG3P6H0r6ab6H3CPpxGaXtSwkdUh6WtLD+dx1XWeStknaKGm9pLU5zfeOGhzAtQBJHcDXgWnAaOAy\nSaObW6rSuAuY2iXtS8BjEfE+4LF8bsfvIDA3IkYD5wF/k/+OXd/1dQCYHBHnAGOBqZLOA24GvhoR\nZwG7gaubWMayuRZ4purcdd03JkXE2KqlQ3zvqMEBXGuYAGyJiOcj4k1gEXBRk8tUChGxEtjVJfki\nYGF+vhC4uKGFKqmI+FVEPJWf7yX9wxuC67uuInktn56QHwFMBv49p7ue60TSUOAvgG/nc+G6bhTf\nO2pwANcahgD/U3X+Uk6zvjE4In6Vn+8ABjezMGUkaTgwDvgpru+6y11664GdwHJgK7AnIg7mLL6H\n1M9twBeBt/P5q+CUugAABXhJREFUu3Fd94UAfiBpnaRZOc33jhr6NbsAZs0UESHJU7HrSNJA4H7g\nuoj4TWqwSFzf9RERh4Cxkk4BFgN/1OQilZKk6cDOiFgn6fxml6fkPhIR2yWdASyX9Gz1i753HMkt\ncK1hOzCs6nxoTrO+8Yqk9wDk484ml6c0JJ1ACt7+NSIeyMmu7z4SEXuAFcCfAKdIqnwp9z2kPv4U\nmCFpG2loy2Tga7iu6y4itufjTtKXkgn43lGTA7jW8CTwvjyz6UTgM8CSJpepzJYAV+bnVwIPNrEs\npZHHBt0JPBMR/1T1kuu7jiSdnlvekHQSMIU03nAFcGnO5nqug4j4ckQMjYjhpPvyDyPiclzXdSXp\nHZIGVZ4DFwCb8L2jJi/k2yIkXUgaa9EBLIiIm5pcpFKQ9D3gfOA04BXg74H/AO4FzgReBD4VEV0n\nOtgxkvQR4MfARjrHC11PGgfn+q4TSR8kDejuIH0Jvzci/kHSCFIr0buAp4ErIuJA80paLrkL9QsR\nMd11XV+5Phfn037Av0XETZLeje8dPXIAZ2ZmZlYw7kI1MzMzKxgHcGZmZmYF4wDOzMzMrGAcwJmZ\nmZkVjAM4MzMzs4JxAGdmpSPpakmR97GsTr85p1/RJX1KTp9YxzKcn99zTL3e08yswgGcmZXRE/nY\nNSCbCLzeQ/oBYF0fl8vMrC4cwJlZGT0L7KIqUMvbfH0YuJvuA7h1XozVzIrCAZyZlU6kFcpXcXig\nNi4fvwGMqdq65/eAc4HHKxklXSRpraT9knZIuiUHgFTlGSNpqaS9+XGfpN+vVS5Jn5F0QNKcfD5U\n0r2Sdkp6Q9JWSf943BVgZqXnAM7MyuoJYGzeLxTShu/rSHss/h8paAP4APBOcgAn6VPAA8AaYAZw\nIzALmF95Y0ln5fwDgCuAq/L7PJT3hD2CpL8itf7Njohv5uS7gWH5/acBNwH9j+9jm1k76NfsApiZ\n9ZHHgROAPwZWklrjVkVESFqdzx+ls5XuiRx83QrcHRGfq7yRpAPA1yXNj4j/Je2puwOYFhFv5jw/\nI3XdXggsrS6IpGuArwF/GRGLql6aAFwWEQ/l8x/V68ObWbm5Bc7MyupJ4CCdAdpEUrcqwOou6Zsj\n4lVgFGnj7Hsl9as8gB+SWtsqM0r/nLT59ttVeV4AtpHG2VX7W+A24NNdgjeA9cB8SVdJOvN4P7CZ\ntQ8HcGZWShHxOilAmpiXExlK5+zUVcB5ucVtIp3j307Lx+8Db1U9Xsjpw6ryzeuS5y1gRFWeikuA\nLcBj3RTz08Ba4KvAi5LWS/ro7/J5zay9uAvVzMrsceByUpC2LSJ25PQ1wCDgfOAs4JacvisfZwFP\nd/N+L1TlWwx8u5s8v+5yfjnwTWCJpGkRsb/yQkRsB67KEykmADfkfGfmrlozs245gDOzMnsCuBa4\nks7uUyLiN5J+DnwhJ1Va4H4JbAeGR8S3arzvY6RJC+vyjNdaXgI+CvwYuF/SxRHxVnWGiHgbWC3p\nxlzm9wIO4MysRw7gzKzMKl2m00iBXLVVwF8Du4FnIAVSkuYC35F0MrAMeJPUNXoxcGnumr2B1Iq3\nVNICUqvbEGAKcFdE/Kj6F0XE85KmAP8FfFfSZaQWwP8kzUR9jjT7dC5pcsQzdfr8ZlZSHgNnZqUV\nES8B/w2Iqha4bFUlvboVLSLuAS4CxgL3kZYU+RzwFCmYIyKeA84j7epwBynQu5G0m8OWHsryC+AC\n4GPAt4D9wEZSYLkEWJjf74KIeOP4PrmZlZ2O3vpvZmZmZq3ELXBmZmZmBeMAzszMzKxgHMCZmZmZ\nFYwDODMzM7OCcQBnZmZmVjAO4MzMzMwKxgGcmZmZWcE4gDMzMzMrGAdwZmZmZgXz/24bDGr3Di9v\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(production,c='blue',lw=2,marker='o',markersize=10)\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Weeks\",fontsize=15)\n",
    "plt.ylabel(\"Production (tons)\",fontsize=15)\n",
    "plt.hlines(y=production.mean(),xmin=-2,xmax=54,color='red',linestyle='--',lw=3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "hMisk5v3umZM"
   },
   "outputs": [],
   "source": [
    "n = len(production)\n",
    "m = production.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1506,
     "status": "ok",
     "timestamp": 1567211402671,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "uXeImgLCumZO",
    "outputId": "e4c0ae30-25ca-4497-92c1-f4d42e6a4f1f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.14423961910034"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "production.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1496,
     "status": "ok",
     "timestamp": 1567211402671,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "rNII4IARumZQ",
    "outputId": "2daf79cc-ee3e-476d-af24-2f0b93011c2e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5747026324798318\n"
     ]
    }
   ],
   "source": [
    "std_err=production.std()/np.sqrt(n)\n",
    "print(std_err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1491,
     "status": "ok",
     "timestamp": 1567211402672,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "tjCO4IQBumZU",
    "outputId": "5a599449-94f2-4646-e55e-6be4bae00b0e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90% confidence interval of mean from  17.920587812526996  to  19.845484342391423\n"
     ]
    }
   ],
   "source": [
    "confidence = 0.9\n",
    "h = std_err * stats.t.ppf((1 + confidence) / 2, n)\n",
    "i90 =[m-h,m+h]\n",
    "print(\"90% confidence interval of mean from \",m-h,\" to \",m+h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1484,
     "status": "ok",
     "timestamp": 1567211402672,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "Ww8G6CVmumZX",
    "outputId": "4b4a7bdf-33c7-4a7a-8a78-00f811ae6f72"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99% confidence interval of mean from  17.346434321376396  to  20.419637833542023\n"
     ]
    }
   ],
   "source": [
    "confidence = 0.99\n",
    "h = std_err * stats.t.ppf((1 + confidence) / 2, n)\n",
    "i99 =[m-h,m+h]\n",
    "print(\"99% confidence interval of mean from \",m-h,\" to \",m+h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1477,
     "status": "ok",
     "timestamp": 1567211402672,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "TUkK7WPfumZZ",
    "outputId": "75861ce1-7970-419a-e3cc-d404daddd87c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17.920587812526996, 19.845484342391423)"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i90[0],i90[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1471,
     "status": "ok",
     "timestamp": 1567211402673,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "mWojRg6PumZb",
    "outputId": "2721d35c-0322-4180-c406-0aa4f712eec2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(17.346434321376396, 20.419637833542023)"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i99[0],i99[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yyikuQkG6LnN"
   },
   "source": [
    "### Repeat the random process many times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pQyXDKYhumZd"
   },
   "outputs": [],
   "source": [
    "def repeat(n):\n",
    "    means = []\n",
    "    interval_90 = []\n",
    "    interval_99 = []\n",
    "    \n",
    "    for i in range(n):\n",
    "        num_weeks = 52\n",
    "        production = np.random.normal(loc=20,scale=5,size=num_weeks)\n",
    "        means.append(production.mean())\n",
    "        if i90[0] <= production.mean() <= i90[1]:\n",
    "            interval_90.append(production.mean())\n",
    "        if i99[0] <= production.mean() <= i99[1]:\n",
    "            interval_99.append(production.mean())\n",
    "    return (interval_90,interval_99,np.array(means))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HTb5JIMwumZf"
   },
   "outputs": [],
   "source": [
    "repeatations = 500\n",
    "int_90,int_99,_ = repeat(repeatations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1458,
     "status": "ok",
     "timestamp": 1567211402674,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "DtUlX-6fumZh",
    "outputId": "0bb67e2a-9903-493a-a2a4-3677fe94b8c3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.384"
      ]
     },
     "execution_count": 13,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(int_90)/repeatations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1452,
     "status": "ok",
     "timestamp": 1567211402674,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "VrJpX6L8umZk",
    "outputId": "a6ddbf00-a448-46bd-b2b4-630e90193254"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.694"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(int_99)/repeatations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yovwMvqkumZm"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e-rPhyGfumZn"
   },
   "source": [
    "## Random choice, shuffling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1445,
     "status": "ok",
     "timestamp": 1567211402674,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "FimYo7aiumZn",
    "outputId": "4fd09922-16e4-4b27-cefb-7fe139674032"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 3, 3, 2, 0, 0, 2, 2, 3, 2, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(4, 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1440,
     "status": "ok",
     "timestamp": 1567211402675,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "4FNjK8w3umZp",
    "outputId": "dfbc249e-e117-437c-fba5-cd99e55a095c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 0, 0, 3, 0, 3, 3, 0, 3, 0, 3])"
      ]
     },
     "execution_count": 16,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(4, 12, p=[.4, .1, .1, .4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 158
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1434,
     "status": "ok",
     "timestamp": 1567211402675,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "NsW9DtivumZs",
    "outputId": "b9fcf581-f7bd-4a7e-c433-3df217be47db"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 9, 1, 3, 9, 9, 9, 2, 7, 4, 3, 1],\n",
       "       [9, 0, 4, 1, 4, 6, 0, 0, 2, 5, 4, 4],\n",
       "       [8, 2, 9, 0, 4, 7, 1, 3, 6, 8, 8, 7],\n",
       "       [0, 9, 7, 6, 7, 7, 6, 6, 9, 8, 9, 4],\n",
       "       [5, 1, 0, 9, 9, 6, 7, 5, 1, 7, 7, 6],\n",
       "       [7, 7, 0, 6, 4, 1, 5, 1, 8, 7, 8, 7],\n",
       "       [1, 6, 1, 5, 4, 5, 2, 6, 7, 0, 0, 0],\n",
       "       [6, 4, 8, 9, 0, 4, 3, 3, 9, 6, 3, 1]])"
      ]
     },
     "execution_count": 17,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randint(0, 10, (8, 12))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1635,
     "status": "ok",
     "timestamp": 1567211402882,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "GtAsw6kXumZu",
    "outputId": "7a3f3c9b-285f-4aa5-d576-4ac41062d09d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 3, 9, 6, 6, 3, 8, 0, 9, 4, 7, 8])"
      ]
     },
     "execution_count": 18,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling individual elements\n",
    "np.random.choice(x.ravel(), 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 87
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1630,
     "status": "ok",
     "timestamp": 1567211402883,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "nq_vnlEeumZx",
    "outputId": "e93a2b25-268a-4596-a7f4-8a5132672472"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 1, 0, 9, 9, 6, 7, 5, 1, 7, 7, 6],\n",
       "       [9, 0, 4, 1, 4, 6, 0, 0, 2, 5, 4, 4],\n",
       "       [7, 7, 0, 6, 4, 1, 5, 1, 8, 7, 8, 7],\n",
       "       [1, 6, 1, 5, 4, 5, 2, 6, 7, 0, 0, 0]])"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling rows\n",
    "idx = np.random.choice(x.shape[0], 4)\n",
    "x[idx, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 158
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1623,
     "status": "ok",
     "timestamp": 1567211402883,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "oNWeKREHumZ1",
    "outputId": "39049b00-6bbf-49ee-e439-f3c1e4762bda"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 2, 9, 1],\n",
       "       [5, 0, 0, 4],\n",
       "       [8, 3, 2, 7],\n",
       "       [8, 6, 9, 4],\n",
       "       [7, 5, 1, 6],\n",
       "       [7, 1, 7, 7],\n",
       "       [0, 6, 6, 0],\n",
       "       [6, 3, 4, 1]])"
      ]
     },
     "execution_count": 20,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling columns\n",
    "idx = np.random.choice(x.shape[1], 4)\n",
    "x[:, idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 158
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1618,
     "status": "ok",
     "timestamp": 1567211402884,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "vXoYxde6umZ3",
    "outputId": "4c452ff2-1a67-402d-b126-7ce09358002d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 2, 9, 0, 4, 7, 1, 3, 6, 8, 8, 7],\n",
       "       [6, 4, 8, 9, 0, 4, 3, 3, 9, 6, 3, 1],\n",
       "       [0, 9, 7, 6, 7, 7, 6, 6, 9, 8, 9, 4],\n",
       "       [9, 0, 4, 1, 4, 6, 0, 0, 2, 5, 4, 4],\n",
       "       [7, 7, 0, 6, 4, 1, 5, 1, 8, 7, 8, 7],\n",
       "       [5, 1, 0, 9, 9, 6, 7, 5, 1, 7, 7, 6],\n",
       "       [0, 9, 1, 3, 9, 9, 9, 2, 7, 4, 3, 1],\n",
       "       [1, 6, 1, 5, 4, 5, 2, 6, 7, 0, 0, 0]])"
      ]
     },
     "execution_count": 21,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Shuffling occurs \"in place\" for efficiency and only along the first axis for multi-dimensional arrays\n",
    "np.random.shuffle(x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 158
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1612,
     "status": "ok",
     "timestamp": 1567211402884,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "dhz56j61umZ5",
    "outputId": "67b4c218-61c1-439c-aabf-b9baec365710"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 0, 9, 8, 4, 8, 7, 2, 8, 1, 3, 7],\n",
       "       [9, 9, 8, 3, 0, 6, 1, 4, 6, 3, 3, 4],\n",
       "       [9, 6, 7, 9, 7, 0, 4, 9, 8, 6, 6, 7],\n",
       "       [2, 1, 4, 4, 4, 9, 4, 0, 5, 0, 0, 6],\n",
       "       [8, 6, 0, 8, 4, 7, 7, 7, 7, 5, 1, 1],\n",
       "       [1, 9, 0, 7, 9, 5, 6, 1, 7, 7, 5, 6],\n",
       "       [7, 3, 1, 3, 9, 0, 1, 9, 4, 9, 2, 9],\n",
       "       [7, 5, 1, 0, 4, 1, 0, 6, 0, 2, 6, 5]])"
      ]
     },
     "execution_count": 22,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To shuffle columns instead, transpose before shuffling\n",
    "np.random.shuffle(x.T)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WMZZf_zvumZ7"
   },
   "source": [
    "### Bootstrapping example (3000 samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 269
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1811,
     "status": "ok",
     "timestamp": 1567211403089,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "DpTkTKmaumZ7",
    "outputId": "447c92f2-a33d-4b64-8611-d4bfb8561dac"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3Wul6SfYkmUsyt7i4OGoZkqRXsdqgP5rkIoD2fqy1HwGml/Tb1tr+P1W1t6pmq2p2ampq\nlWVIkpaz2qA/AOxq07uAu5a0f6SdfXM58KLj85I0Wcv+GJvkSwx+eL0gyQLwWeBzwB1JdgOHgGtb\n97uBq4F54CXghjWoWZK0AsOcdfOhV1m04yR9C7hx1KIkSePjlbGS1DmDXpI6Z9BLUucMeknqnEEv\nSZ0z6CWpcwa9tIZGufuld77UuPiEqQmZmb6QQwve2bB3o9z90jtfalwM+gnxcYCSThWHbiSpcwa9\nJHXOoJekzhn00jrlGTsaF3+MldYpz9jRuHhEP4KZ6QtXfcQlrSW/DWgpj+hH4CmSWq/8NqCl1uSI\nPsmVSb6fZD7JTWuxDUlrY5RvA34jWJ/GfkSf5DTg3wHvBRaAbyc5UFVPjHtbksZvlG8D4DeC9Wgt\njugvA+ar6umq+inwZWDnGmxHkjSEtQj6rcDhJfMLrU3S68AoQz9nn3XaRNbtfbgpg+d5j/EDkw8A\nV1bVP23zHwZ+pao+ekK/PcCeNvsW4Pur2NwFwF+OUO564X6sHz3sA/SxHz3sA6ztfvytqppartNa\nnHVzBJheMr+ttf2cqtoL7B1lQ0nmqmp2lM9YD9yP9aOHfYA+9qOHfYD1sR9rMXTzbWB7kouTnAFc\nBxxYg+1IkoYw9iP6qnolyUeB/wycBvxhVT0+7u1IkoazJhdMVdXdwN1r8dknGGnoZx1xP9aPHvYB\n+tiPHvYB1sF+jP3HWEnS+uK9biSpc90EfZJPJqkkF0y6ltVI8m+TfC/Jo0m+lmTzpGsaVg+3vEgy\nneS+JE8keTzJxyZd02olOS3Jw0m+PulaVivJ5iR3tn8TTyZ516RrWo0kv93+Pn03yZeSnDWJOroI\n+iTTwK8BP5h0LSO4B3hbVf0d4L8Dn55wPUNZcsuLq4BLgA8luWSyVa3KK8Anq+oS4HLgxg26HwAf\nA56cdBEj+gLwjap6K/B2NuD+JNkK/BYwW1VvY3ByynWTqKWLoAduBn4H2LA/OFTVN6vqlTZ7P4Pr\nDzaCLm55UVXPVNVDbfqvGATLhruiO8k24NeBL066ltVKcg7wq8A+gKr6aVW9MNmqVm0T8IYkm4A3\nAv9zEkVs+KBPshM4UlXfmXQtY/RPgP806SKG1N0tL5LMAO8EHphsJavy+wwOev560oWM4GJgEfij\nNgT1xSRnT7qolaqqI8DvMhhpeAZ4saq+OYlaNkTQJ/mzNsZ14msn8BngX066xmEssx/H+/wLBsMI\nI9w/UKuV5BeAPwU+XlU/nHQ9K5HkfcCxqnpw0rWMaBNwKXBrVb0T+BGw4X77SXIug2+3FwO/DJyd\n5B9NopYN8eCRqnrPydqT/G0Gf4jfyeCpTduAh5JcVlXPnsISh/Jq+3Fckn8MvA/YURvnvNehbnmx\nESQ5nUHI315VX510PatwBfD+JFcDZwG/mORPqmoi4TKCBWChqo5/o7qTDRj0wHuAv6iqRYAkXwX+\nHvAnp7qQDXFE/2qq6rGq+qWqmqmqGQZ/QS5djyG/nCRXMvjK/f6qemnS9axAF7e8yOBIYR/wZFX9\n3qTrWY2q+nRVbWv/Fq4D7t2AIU/793s4yVta0w5gIz7P4gfA5Une2P5+7WBCPypviCP614k/AM4E\n7mnfTu6vqn8+2ZKW19EtL64APgw8luSR1vaZdpW3Tr3fBG5vBw9PAzdMuJ4Vq6oHktwJPMRgOPZh\nJnSVrFfGSlLnNvTQjSRpeQa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0md+79gOEF2Z6Ym\n0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.concatenate([np.random.exponential(size=2000), np.random.normal(size=1000)])\n",
    "plt.hist(x, 20,edgecolor='k',color='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0j0X-OAKumZ9"
   },
   "outputs": [],
   "source": [
    "n = len(x)\n",
    "reps = 10000\n",
    "\n",
    "# Bootstrapping n-samples from array x with replacements many times (reps=10000) \n",
    "xb = np.random.choice(x, (n, reps))\n",
    "# Mean of the bootstrappen arrays\n",
    "mb = xb.mean(axis=0)\n",
    "# Sort the array of means\n",
    "mb.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3142,
     "status": "ok",
     "timestamp": 1567211404433,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "_VKX7sSSumZ_",
    "outputId": "4c50ded3-4547-43a1-c213-614e3e7526f4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.63485132, 0.7038538 ])"
      ]
     },
     "execution_count": 25,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute percentile for 90% confidence interval\n",
    "np.percentile(mb, [5, 95])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3136,
     "status": "ok",
     "timestamp": 1567211404433,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "hAp0qZO5umaE",
    "outputId": "9cee6358-e015-4d74-fe4b-ae122667b1d2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.61583156, 0.72358553])"
      ]
     },
     "execution_count": 26,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute percentile for 99% confidence interval\n",
    "np.percentile(mb, [0.5, 99.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zfayMqFUumaG"
   },
   "source": [
    "### Same underlying process but only 300 samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XG1Uxw3rumaH"
   },
   "outputs": [],
   "source": [
    "x = np.concatenate([np.random.exponential(size=200), np.random.normal(size=100)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8jSxrj6yumaJ"
   },
   "outputs": [],
   "source": [
    "n = len(x)\n",
    "reps = 10000\n",
    "\n",
    "# Bootstrapping n-samples from array x with replacements many times (reps=10000) \n",
    "xb = np.random.choice(x, (n, reps))\n",
    "# Mean of the bootstrappen arrays\n",
    "mb = xb.mean(axis=0)\n",
    "# Sort the array of means\n",
    "mb.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3121,
     "status": "ok",
     "timestamp": 1567211404434,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "LAvAcZsjumaL",
    "outputId": "3d061d1b-0fcd-4744-b54f-bd7669fb5c98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.55701889, 0.76816666])"
      ]
     },
     "execution_count": 29,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute percentile for 90% confidence interval\n",
    "np.percentile(mb, [5, 95])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3115,
     "status": "ok",
     "timestamp": 1567211404435,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "-RjWdhYhumaO",
    "outputId": "577ecca7-6b25-443c-9925-0c9562ad4782"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4984252 , 0.83334772])"
      ]
     },
     "execution_count": 30,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute percentile for 99% confidence interval\n",
    "np.percentile(mb, [0.5, 99.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FaKQleVx--Iu"
   },
   "source": [
    "## Hypothesis testing\n",
    "\n",
    "### The process\n",
    "\n",
    "Statistical hypothesis testing reflects **the scientific method, adapted to the setting of research involving data analysis**. In this framework, a researcher makes a precise statement about the population of interest, then aims to falsify the statement. \n",
    "\n",
    "In statistical hypothesis testing, the statement in question is the **null hypothesis**. If we reject the null hypothesis, we have falsified it (to some degree of confidence). \n",
    "\n",
    "According to the scientific method, falsifying a hypothesis should require an overwhelming amount of evidence against it. If the data we observe are ambiguous, or are only weakly contradictory to the null hypothesis, we do not reject the null hypothesis.\n",
    "\n",
    "Basis of hypothesis testing has two attributes:\n",
    "\n",
    "**Null Hypothesis: $H_0$**\n",
    "\n",
    "**Alternative Hypothesis: $H_a$**\n",
    "\n",
    "Various cases which are generally used in hypothesis testing are:\n",
    "\n",
    "* One Population Proportion\n",
    "* Difference in Population Proportions\n",
    "* One Population Mean\n",
    "* Difference in Population Means\n",
    "\n",
    "The equation to compute the ***test statistic*** is:\n",
    "\n",
    "$$test\\ statistic = \\frac{Best\\ Estimate - Hypothesized\\ Estimate}{Standard\\ Error\\ of\\ Estimate}$$\n",
    "\n",
    "After computing this _test statistic_, we ask ourselves, \"How likely is it to see this value of the test statistic under the Null hypothesis?\" i.e. we compute a probability value.\n",
    "\n",
    "Depending on that probability, we either **reject or fail to reject the null hypothesis**. Note, we **do not accept the alternate hypothesis** because we can never ovserve all the data in the universe.\n",
    "\n",
    "### Type-I and Type-II errors\n",
    "\n",
    "The framework of formal hypothesis testing defines two distinct types of errors. A **type I error (false positive)** occurs when the null hypothesis is true but is incorrectly rejected. A **type II error** occurs when the null hypothesis is not rejected when it actually is false. \n",
    "\n",
    "Most traditional methods for statistical inference aim to strictly control the probability of a type I error, usually at 5%. While we also wish to minimize the probability of a type II error, this is a secondary priority to controlling the type I error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "diz4wE6sumaR"
   },
   "source": [
    "### Let us simulate James Bond's Martini guessing!\n",
    "\n",
    "![bond_martini](https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/bond_martini.PNG)\n",
    "\n",
    "Suppose we gave Mr. Bond a series of 16 taste tests. In each test, we flipped a fair coin to determine whether to stir or shake the martini.\n",
    "\n",
    "Then we presented the martini to Mr. Bond and asked him to decide whether it was shaken or stirred. Let's say Mr. Bond was correct on 13 of the 16 taste tests.\n",
    "\n",
    "**Does this prove that Mr. Bond has at least some ability to tell whether the martini was shaken or stirred?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GLWRP7MBumaS"
   },
   "outputs": [],
   "source": [
    "martini = ['shaken','stirred']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "I2cZLU_mumaU"
   },
   "outputs": [],
   "source": [
    "glasses = []\n",
    "for _ in range(16):\n",
    "    glasses.append(np.random.choice(martini))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 364,
     "status": "ok",
     "timestamp": 1567291952087,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "0KVC5gIJumaV",
    "outputId": "07caf998-a963-4f2c-d115-618cb0d92f73"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shaken, stirred, shaken, shaken, shaken, stirred, shaken, shaken, stirred, stirred, stirred, shaken, stirred, shaken, stirred, shaken, "
     ]
    }
   ],
   "source": [
    "for g in glasses:\n",
    "    print(g,end=', ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sZS1Xc5zumaX"
   },
   "source": [
    "### A function to generate Mr. Bond's response (when he is randomly guessing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MtJjpY6wumaY"
   },
   "outputs": [],
   "source": [
    "def bond_guess(n,verbose=True):\n",
    "    score=[]\n",
    "    for _ in range(n):\n",
    "        bond_answers = []\n",
    "        for _ in range(16):\n",
    "            bond_answers.append(np.random.choice(martini))\n",
    "        if verbose:\n",
    "            print(\"My name is Bond...James Bond, and I say the glasses are as follows:\",bond_answers)\n",
    "        correct_guess = np.sum(np.array(bond_answers)==np.array(glasses))\n",
    "        if verbose:\n",
    "            print(\"\\nMr. James Bond gave {} correct answers\".format(correct_guess))\n",
    "            print(\"-\"*100)\n",
    "        score.append(correct_guess)\n",
    "    return np.array(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hFB7rVywumaZ"
   },
   "source": [
    "### Print 5 typical responses when Mr. Bond is randomly guessing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 383
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 338,
     "status": "ok",
     "timestamp": 1567291970980,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "mLwc7fGbumaa",
    "outputId": "b6c6ce94-9a4c-49f0-dc30-6b9f1affc394"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "My name is Bond...James Bond, and I say the glasses are as follows: ['shaken', 'shaken', 'stirred', 'stirred', 'shaken', 'stirred', 'stirred', 'stirred', 'stirred', 'shaken', 'stirred', 'shaken', 'shaken', 'stirred', 'stirred', 'shaken']\n",
      "\n",
      "Mr. James Bond gave 8 correct answers\n",
      "----------------------------------------------------------------------------------------------------\n",
      "My name is Bond...James Bond, and I say the glasses are as follows: ['stirred', 'stirred', 'shaken', 'shaken', 'shaken', 'shaken', 'stirred', 'shaken', 'stirred', 'shaken', 'stirred', 'shaken', 'stirred', 'shaken', 'stirred', 'stirred']\n",
      "\n",
      "Mr. James Bond gave 11 correct answers\n",
      "----------------------------------------------------------------------------------------------------\n",
      "My name is Bond...James Bond, and I say the glasses are as follows: ['shaken', 'stirred', 'stirred', 'stirred', 'stirred', 'stirred', 'shaken', 'stirred', 'stirred', 'stirred', 'stirred', 'shaken', 'stirred', 'shaken', 'stirred', 'shaken']\n",
      "\n",
      "Mr. James Bond gave 12 correct answers\n",
      "----------------------------------------------------------------------------------------------------\n",
      "My name is Bond...James Bond, and I say the glasses are as follows: ['shaken', 'shaken', 'stirred', 'shaken', 'stirred', 'shaken', 'shaken', 'shaken', 'stirred', 'shaken', 'shaken', 'shaken', 'shaken', 'stirred', 'stirred', 'shaken']\n",
      "\n",
      "Mr. James Bond gave 8 correct answers\n",
      "----------------------------------------------------------------------------------------------------\n",
      "My name is Bond...James Bond, and I say the glasses are as follows: ['shaken', 'shaken', 'stirred', 'shaken', 'stirred', 'stirred', 'shaken', 'shaken', 'shaken', 'shaken', 'shaken', 'shaken', 'stirred', 'stirred', 'stirred', 'shaken']\n",
      "\n",
      "Mr. James Bond gave 9 correct answers\n",
      "----------------------------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "_=bond_guess(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wvcKVPyGumab"
   },
   "source": [
    "### Compute the probability of score >=13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1070,
     "status": "ok",
     "timestamp": 1567292013059,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "Xk3s8Tzhumac",
    "outputId": "f9ecda00-0cf8-47bf-f372-0f0e445e432f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0092\n"
     ]
    }
   ],
   "source": [
    "score = bond_guess(10000,verbose=False)\n",
    "print(np.sum(score>=13)/10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RfPEOvljumad"
   },
   "source": [
    "### Show probabilities of all the correct guesses (1-16) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 311
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1045,
     "status": "ok",
     "timestamp": 1567292028522,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "K4VvIeTFumae",
    "outputId": "9cda46f5-e5a9-4f58-c420-2a323c350e55"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of answering 0 correct: 0.0\n",
      "Probability of answering 1 correct: 0.0003\n",
      "Probability of answering 2 correct: 0.003\n",
      "Probability of answering 3 correct: 0.0091\n",
      "Probability of answering 4 correct: 0.0259\n",
      "Probability of answering 5 correct: 0.0649\n",
      "Probability of answering 6 correct: 0.1194\n",
      "Probability of answering 7 correct: 0.1774\n",
      "Probability of answering 8 correct: 0.1953\n",
      "Probability of answering 9 correct: 0.176\n",
      "Probability of answering 10 correct: 0.119\n",
      "Probability of answering 11 correct: 0.0686\n",
      "Probability of answering 12 correct: 0.0295\n",
      "Probability of answering 13 correct: 0.0094\n",
      "Probability of answering 14 correct: 0.0018\n",
      "Probability of answering 15 correct: 0.0004\n",
      "Probability of answering 16 correct: 0.0\n"
     ]
    }
   ],
   "source": [
    "score = bond_guess(10000,verbose=False)\n",
    "prob = []\n",
    "guess = []\n",
    "for i in range(17):\n",
    "    print(f\"Probability of answering {i} correct: {np.sum(score==i)/10000}\")\n",
    "    prob.append(np.sum(score==i)/10000)\n",
    "    guess.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 345
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 511,
     "status": "ok",
     "timestamp": 1567292031180,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "o3yYM7iCEoGt",
    "outputId": "1599e8ea-e142-4519-d45d-914c2576e998"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wocsRGWNSWJJkjHGN7wzbffr0oWjRoi5G447ixYvTp08f7/rEiRNdjMYY48uSJGOMK3bt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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,5))\n",
    "plt.plot(guess,prob,c='k',lw=3)\n",
    "plt.xlabel(\"Number of exactly these many correct guesses\",fontsize=14)\n",
    "plt.ylabel(\"Probability\",fontsize=14)\n",
    "plt.xticks(guess,fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.hlines(y=0.05,xmin=0,xmax=16,color='blue',linestyle='--')\n",
    "plt.text(s=\"p-value 0.05\",x=6,y=0.07,fontsize=16,color='red')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tiZLwbyWumag"
   },
   "source": [
    "### Show probabilities of _at least_ certain number of correct guesses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 294
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1072,
     "status": "ok",
     "timestamp": 1567292167522,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "jAkqWRwQumag",
    "outputId": "4c012881-0656-4ff6-da21-30afdf15b935"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of answering at least 1 correct: 1.0\n",
      "Probability of answering at least 2 correct: 0.9997\n",
      "Probability of answering at least 3 correct: 0.998\n",
      "Probability of answering at least 4 correct: 0.9896\n",
      "Probability of answering at least 5 correct: 0.9596\n",
      "Probability of answering at least 6 correct: 0.8916\n",
      "Probability of answering at least 7 correct: 0.7767\n",
      "Probability of answering at least 8 correct: 0.6003\n",
      "Probability of answering at least 9 correct: 0.4045\n",
      "Probability of answering at least 10 correct: 0.2255\n",
      "Probability of answering at least 11 correct: 0.1062\n",
      "Probability of answering at least 12 correct: 0.0406\n",
      "Probability of answering at least 13 correct: 0.0117\n",
      "Probability of answering at least 14 correct: 0.0024\n",
      "Probability of answering at least 15 correct: 0.0002\n",
      "Probability of answering at least 16 correct: 0.0\n"
     ]
    }
   ],
   "source": [
    "score = bond_guess(10000,verbose=False)\n",
    "prob = []\n",
    "guess = []\n",
    "for i in range(1,17):\n",
    "    print(f\"Probability of answering at least {i} correct: {np.sum(score>=i)/10000}\")\n",
    "    prob.append(np.sum(score>=i)/10000)\n",
    "    guess.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 345
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 515,
     "status": "ok",
     "timestamp": 1567292170225,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "XwaIi9EKBbIe",
    "outputId": "b2d3c618-eed3-445e-feb6-ac6c80dd75ea"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iIpHsxhtvpFmzZgAkJyfTvXt3nHM+ZyUi2TmZi/hdZ2aLzWyHmW03s0Vm1iIU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\nKa5x2TQurQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,5))\n",
    "plt.plot(guess,prob,c='k',lw=3)\n",
    "plt.xlabel(\"Number of at least these many correct guesses\",fontsize=14)\n",
    "plt.ylabel(\"Probability\",fontsize=14)\n",
    "plt.xticks(guess,fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.hlines(y=0.05,xmin=0,xmax=16,color='blue',linestyle='--')\n",
    "plt.text(s=\"p-value 0.05\",x=4,y=0.15,fontsize=16,color='red')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QXe773qPAv-J"
   },
   "source": [
    "### What can we deduce from this probability distribution?\n",
    "\n",
    "If we are going with p=0.05 or 95% significance level, then we can conclude that anything above 12 correct answers are unlikely if Mr. Bond was guessing randomly. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TBbQytkq8iXA"
   },
   "source": [
    "## Hypothesis testing alternative example with population proportions\n",
    "<br>\n",
    "<img src=\"https://raw.githubusercontent.com/tirthajyoti/Stats-Maths-with-Python/master/images/Hypothesis_test.jpg\" width=600 height=420></img>\n",
    "\n",
    "### Research Question\n",
    "\n",
    "*Is there a significant difference between the population proportions of parents of Black children and parents of Hispanic children who report that their child has had some swimming lessons*? (**A real-life study from the Univ. of Michigan**)\n",
    "\n",
    "### Formulation\n",
    "\n",
    "***Populations***: All parents of black children age 6-18 and all parents of Hispanic children age 6-18  \n",
    "***Parameter of Interest***: p1 - p2, where p1 = black and p2 = hispanic  \n",
    "\n",
    "***Null Hypothesis:*** p1 - p2 = 0  \n",
    "***Alternative Hypthosis:*** p1 - p2 $\\neq$ 0\n",
    "\n",
    "### Data\n",
    "\n",
    "247 Parents of Black Children\n",
    "36.8% of parents report that their child has had some swimming lessons.\n",
    "\n",
    "308 Parents of Hispanic Children\n",
    "38.9% of parents report that their child has had some swimming lessons.\n",
    "\n",
    "### Function used in the code\n",
    "\n",
    "[Numpy Binomial distribution](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.binomial.html) because this is a matter of YES/NO answers (from the parents)\n",
    "\n",
    "[Scipy independent t-test](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html) because we are interested in a two-sided test of equal/unequal means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Qw7Gxize9Kmb"
   },
   "outputs": [],
   "source": [
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rZpS2CSj8yLz"
   },
   "outputs": [],
   "source": [
    "n1 = 247\n",
    "p1 = .37\n",
    "\n",
    "n2 = 308\n",
    "p2 = .39\n",
    "\n",
    "population1 = np.random.binomial(1, p1, n1)\n",
    "population2 = np.random.binomial(1, p2, n2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 138
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 348,
     "status": "ok",
     "timestamp": 1567293099058,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "9urVpKfEFzGj",
    "outputId": "fbccbae7-68ad-4be6-d198-fe74ddcdbbc5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parents of Black children\n",
      "-------------------------------------------------------\n",
      "86 parents answered YES and 161 parents answered NO\n",
      "\n",
      "Parents of Hispanic children\n",
      "-------------------------------------------------------\n",
      "114 parents answered YES and 194 parents answered NO\n"
     ]
    }
   ],
   "source": [
    "print(\"Parents of Black children\")\n",
    "print(\"-\"*55)\n",
    "print(f\"{population1.sum()} parents answered YES and {n1-population1.sum()} parents answered NO\")\n",
    "print(\"\\nParents of Hispanic children\")\n",
    "print(\"-\"*55)\n",
    "print(f\"{population2.sum()} parents answered YES and {n2-population2.sum()} parents answered NO\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "siZnSAlqFxQO"
   },
   "outputs": [],
   "source": [
    "t_stat,pval=scipy.stats.ttest_ind(population1, population2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 320,
     "status": "ok",
     "timestamp": 1567293100903,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "wMIQ1tcS89b5",
    "outputId": "611c5d9a-d53c-4b0e-b6b1-387aeb8b9c58"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The t-statistic from this data: -0.5344882669395735\n",
      "Corresponding p-value from this data: 0.5932185803894023\n"
     ]
    }
   ],
   "source": [
    "print(\"The t-statistic from this data:\",t_stat)\n",
    "print(\"Corresponding p-value from this data:\",pval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 69
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 332,
     "status": "ok",
     "timestamp": 1567292890659,
     "user": {
      "displayName": "Tirthajyoti Sarkar",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mD6d7dlMqdpzL4sermIF1ujmpSRxY2WnE4tuB-UsQ=s64",
      "userId": "01914075970409030121"
     },
     "user_tz": 420
    },
    "id": "JNoPujIA9f_O",
    "outputId": "081a446c-0606-4de7-c46f-5d0aec69f7a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Based on this data, NULL hypothesis cannot be rejected \n",
      "i.e. there is no significant difference between the proportion of Black and Hispanic parents,\n",
      "who reporpted that their children had a swimming lesson\n"
     ]
    }
   ],
   "source": [
    "if pval>0.05:\n",
    "  print(\"Based on this data, NULL hypothesis cannot be rejected \\ni.e. there is no significant difference between the proportion of Black and Hispanic parents,\\nwho reporpted that their children had a swimming lesson\")\n",
    "else:\n",
    "  print(\"There seems to be a statisticlly significant difference in the proportion of Black and Hispanic parents,\\nwho reporpted that their children had a swimming lesson\")"
   ]
  }
 ],
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