{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5b299da0",
   "metadata": {},
   "source": [
    "Lab Example 1 — Sampling variability and CLT\n",
    "\n",
    "Objective: show that individual measurements vary, but sample means are more stable.\n",
    "\n",
    "Students should:\n",
    "\n",
    "1. Generate a non-normal population.\n",
    "2. Take many random samples.\n",
    "3. Compute the mean of each sample.\n",
    "4. Plot the distribution of the sample means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07e7f5cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AgF1yUyJCATAAALAaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAasV83QDAFpFDF+Vp+30jYwusLQCA/6FnBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGC1Yr5887Nnz8oLL7wgs2bNksOHD0vVqlWlV69e8uyzz0pQUJDZxnEcGTZsmLz11lty7NgxadmypUyZMkXq1Knjy6YDFxQ5dFGu99K+kbEF8rp5fW0AsJFPe2ZGjRplgsnEiRPlxx9/NI9Hjx4tb7zxhnsbfTxhwgSZOnWqrF+/XkqXLi0xMTGSlpbmy6YDAAA/4dOembVr10rHjh0lNvb//nKMjIyUDz74QL799lt3r8y4ceNMT41up2bOnCnh4eGycOFC6datmy+bDwAAAr1npkWLFpKQkCA7d+40j7ds2SLffPONtG/f3jzeu3evGX6Kjo52/0xYWJg0a9ZMEhMTs33N9PR0OX78uMcCAAAKL5/2zAwdOtSEjXr16knRokVNDc3LL78sPXr0MM9rkFHaE5OZPnY9l1V8fLwMHz78ErQehUFe608KezsAwEY+7ZmZO3euvP/++zJ79mzZtGmTzJgxQ1577TXz1VtxcXGSmprqXpKTk/O1zQAAwL/4tGfm6aefNr0zrtqXxo0by/79+03vSs+ePSUiIsKsT0lJkSpVqrh/Th9fc8012b5mSEiIWQAAQGDwac/MqVOnpEgRzybocFNGRob5vlatWibQaF2Niw5L6aymqKioS95eAADgf3zaM9OhQwdTI1OjRg1p2LChbN68WcaMGSO9e/c2z+u1ZgYOHCgjRoww15XRcPPcc8+Z69F06tTJl00HAAB+wqdhRq8no+HksccekyNHjpiQ0rdvX3n++efd2wwZMkROnjwpDz/8sLloXqtWrWTJkiVSokQJXzYdAAD4iSBHL+ZSiOmwlE7n1mLg0NBQXzcHfiYQZhFxBWAAhf38zb2ZAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGA1wgwAALAaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWI0wAwAArFbM1w0AULAihy7K9bb7RsYWaFsAoCDQMwMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWM2nYSYyMlKCgoLOWfr162eeT0tLM99XrFhRypQpI126dJGUlBRfNhkAAPgZn4aZDRs2yKFDh9zLsmXLzPq77rrLfB00aJB89tlnMm/ePFm1apUcPHhQOnfu7MsmAwAAP+PT2xlUqlTJ4/HIkSPlyiuvlJtvvllSU1PlnXfekdmzZ0ubNm3M89OmTZP69evLunXrpHnz5j5qNQAA8Cd+UzNz+vRpmTVrlvTu3dsMNSUlJcmZM2ckOjravU29evWkRo0akpiYmOPrpKeny/Hjxz0WAABQePlNmFm4cKEcO3ZMevXqZR4fPnxYihcvLuXKlfPYLjw83DyXk/j4eAkLC3Mv1atXL/C2AwAA3/GbMKNDSu3bt5eqVate1OvExcWZISrXkpycnG9tBAAA/senNTMu+/fvl+XLl8v8+fPd6yIiIszQk/bWZO6d0dlM+lxOQkJCzAIAAAKDX/TMaGFv5cqVJTY21r2uadOmEhwcLAkJCe51O3bskAMHDkhUVJSPWgoAAPyNz3tmMjIyTJjp2bOnFCv2v+ZovUufPn1k8ODBUqFCBQkNDZX+/fubIMNMJgAA4DdhRoeXtLdFZzFlNXbsWClSpIi5WJ7OUoqJiZHJkyf7pJ0AAMA/BTmO40ghplOztZdHi4G1dwfILHLoInZIJvtG/m+oFwBsOX/7Rc0MAACAtwgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGA1wgwAALAaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWI0wAwAArFbM1w0A8lvk0EXsVAAIIPTMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACs5vPrzPz666/yzDPPyOLFi+XUqVNSu3ZtmTZtmlx//fXmecdxZNiwYfLWW2/JsWPHpGXLljJlyhSpU6eOr5sOBPQ1evaNjC3QtgCAFT0zf/zxhwknwcHBJsz88MMP8vrrr0v58uXd24wePVomTJggU6dOlfXr10vp0qUlJiZG0tLSfNl0AADgJ3zaMzNq1CipXr266YlxqVWrlvt77ZUZN26cPPvss9KxY0ezbubMmRIeHi4LFy6Ubt26+aTdAADAf/i0Z+bTTz81w0l33XWXVK5cWa699loznOSyd+9eOXz4sERHR7vXhYWFSbNmzSQxMTHb10xPT5fjx497LAAAoPDyaZjZs2ePu/5l6dKl8uijj8oTTzwhM2bMMM9rkFHaE5OZPnY9l1V8fLwJPK5Fe34AAEDh5dMwk5GRIdddd5288sorplfm4YcfloceesjUx3grLi5OUlNT3UtycnK+thkAAPgXn4aZKlWqSIMGDTzW1a9fXw4cOGC+j4iIMF9TUlI8ttHHrueyCgkJkdDQUI8FAAAUXj4NMzqTaceOHR7rdu7cKTVr1nQXA2toSUhIcD+vNTA6qykqKuqStxcAAPgfn85mGjRokLRo0cIMM919993y7bffyr///W+zqKCgIBk4cKCMGDHC1NVouHnuueekatWq0qlTJ182HQAA+AmfhpkbbrhBFixYYOpcXnzxRRNWdCp2jx493NsMGTJETp48aepp9KJ5rVq1kiVLlkiJEiV82XQAAOAnghy9mEshpsNSOqtJi4GpnwkMebmKLbzHFYAB+Mv5m3szAQAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYzafXmQEQGFPgmcYNoCDRMwMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwWjFfNwCBKXLoojxtv29kbIG1BQBgN3pmAABA4IWZPXv25H9LAAAALlWYqV27trRu3VpmzZolaWlp3rwEAACA78LMpk2bpEmTJjJ48GCJiIiQvn37yrfffps/LQIAACjoMHPNNdfI+PHj5eDBg/Luu+/KoUOHpFWrVtKoUSMZM2aMHD161JuXBQAAuLQFwMWKFZPOnTvLvHnzZNSoUbJr1y556qmnpHr16nL//febkAMAAOC3YWbjxo3y2GOPSZUqVUyPjAaZ3bt3y7Jly0yvTceOHfOvpQAAAPkVZjS4NG7cWFq0aGFCy8yZM2X//v0yYsQIqVWrltx0000yffp0U1tzPi+88IIEBQV5LPXq1XM/r8XF/fr1k4oVK0qZMmWkS5cukpKS4k2TAQBAIeXVRfOmTJkivXv3ll69eplemexUrlxZ3nnnnQu+VsOGDWX58uX/a1Cx/zVp0KBBsmjRIjOMFRYWJo8//rgZ1lqzZo03zQYAAIWQV2Hm559/vuA2xYsXl549e164AcWKmRlRWaWmppowNHv2bGnTpo1ZN23aNKlfv76sW7dOmjdv7k3TAQBAIePVMJOGCu0tyUrXzZgxI8/BqGrVqnLFFVdIjx495MCBA2Z9UlKSnDlzRqKjo93b6hBUjRo1JDEx0ZtmAwCAQsirMBMfHy+XXXZZtkNLr7zySq5fp1mzZqa2ZsmSJWboau/evabe5sSJE3L48GHTu1OuXDmPnwkPDzfP5SQ9PV2OHz/usQAAgMLLq2Em7T3RQt+satas6e5ZyY327du7v9eL8Gm40deYO3eulCxZUrwNWsOHD/fqZwEAQID0zGgPzNatW89Zv2XLFjPzyFvaC3PVVVeZ69VoHc3p06fl2LFjHtvobKbsamxc4uLiTL2Na0lOTva6PQAAoJCGme7du8sTTzwhK1eulLNnz5plxYoVMmDAAOnWrZvXjfnzzz/NdWp0hlTTpk0lODhYEhIS3M/v2LHD9PxERUXl+BohISESGhrqsQAAgMLLq2Gml156Sfbt2ydt27Z1T6XOyMgwV/3NS82MXmSvQ4cOZmhJr1czbNgwKVq0qAlLOhW7T58+5v5PFSpUMKGkf//+JsgwkwkAAFxUmNHC3A8//NCEGh1a0voWvYiehpK8+OWXX0xw+e2336RSpUrm/k467Vq/V2PHjpUiRYqYi+VpYW9MTIxMnjzZmyYD8KHIoYvytP2+kbEF1hYAhY9XYcZF61t08dacOXPO+3yJEiVk0qRJZgEAAMi3MKM1MjqlWutZjhw5YoaYMtP6GQAAAL8NM1roq2EmNjZWGjVqZO6pBAAAYE2Y0eEhvRbM7bffnv8tAgAAKOip2VoAXLt2bW9+FAAAwPdh5sknn5Tx48eL4zj52xoAAIBLMcz0zTffmAvmLV68WBo2bGgubpfZ/PnzvXlZAACASxNm9LYDd9xxhzc/CgAA4PswM23atPxtBQAAwKWsmVF//fWXLF++XN588005ceKEWae3JND7KwEAAPh1z8z+/fvltttuMzd91NsMtGvXTsqWLSujRo0yj6dOnZr/LQUAAMivnhm9aN71118vf/zxh7kvk4vW0WS+yzUAAIBf9sx8/fXXsnbtWnO9mcwiIyPl119/za+2AQAAFEzPjN6LSe/PlN1dsHW4CQAAwK/DzK233irjxo1zP9Z7M2nh77Bhw7jFAQAA8P9hptdff11iYmKkQYMGkpaWJvfcc4/8/PPPctlll8kHH3yQ/61EwIscuijg9wEAIB/DTLVq1WTLli3mhpNbt241vTJ9+vSRHj16eBQEAwAA+GWYMT9YrJjce++9+dsaAACASxFmZs6ced7n77//fm9eFgAA4NKEGb3OTGZnzpyRU6dOmanapUqVIswAAAD/ns2kF8vLvGjNzI4dO6RVq1YUAAMAADvuzZRVnTp1ZOTIkef02gAAAFgRZlxFwXqzSQAAAL+umfn00089HjuOI4cOHZKJEydKy5Yt86ttAAAABRNmOnXq5PFYrwBcqVIladOmjbmgHgAAgF+HGb03EwAAQKGrmQEAALCiZ2bw4MG53nbMmDHevAUAAEDBhZnNmzebRS+WV7duXbNu586dUrRoUbnuuus8amkAAAD8Lsx06NBBypYtKzNmzJDy5cubdXrxvAceeEBuuukmefLJJ/O7nQAAAPlXM6MzluLj491BRun3I0aMYDYTAADw/zBz/PhxOXr06Dnrdd2JEyfyo10AAAAFF2buuOMOM6Q0f/58+eWXX8zy8ccfS58+faRz587evKS5FYLW2AwcONC9Li0tTfr16ycVK1aUMmXKSJcuXSQlJcWr1wcAAIWTV2Fm6tSp0r59e7nnnnukZs2aZtHvb7vtNpk8eXKeX2/Dhg3y5ptvSpMmTTzWDxo0SD777DOZN2+erFq1ytwqwduwBAAACievwkypUqVMaPntt9/cM5t+//13s6506dJ5ei2943aPHj3krbfe8qjBSU1NlXfeecdM7dYrCzdt2lSmTZsma9eulXXr1nnTbAAAUAhd1EXz9H5MuugdszXE6D2a8kqHkWJjYyU6OtpjfVJSkpn6nXl9vXr1pEaNGpKYmJjj66Wnp5uanswLAAAovLwKM9oj07ZtW7nqqqvk9ttvN4FGac1MXqZlz5kzRzZt2mRmRmV1+PBhKV68uJQrV85jfXh4uHkuJ/paYWFh7qV69ep5+t0AAEAAhBmtZQkODpYDBw6YISeXrl27ypIlS3L1GsnJyTJgwAB5//33pUSJEpJf4uLizBCVa9H3AQAAhZdXF8378ssvZenSpVKtWjWP9TrctH///ly9hg4jHTlyxOOKwWfPnpXVq1fLxIkTzeufPn1ajh075tE7o7OZIiIicnzdkJAQswAAgMDgVZg5efKkR4+MixYB5zZI6DDVtm3bPNbpdG+ti3nmmWfM8JD2/iQkJJgp2WrHjh2mNygqKsqbZgMAgELIqzCjtyyYOXOmvPTSS+axXh8mIyNDRo8eLa1bt87Va+jtEBo1auSxTouI9ZoyrvVag6M3taxQoYKEhoZK//79TZBp3ry5N80GAACFkFdhRkOL9qxs3LjRDAUNGTJEtm/fbnpm1qxZk2+NGzt2rBQpUsT0zOgspZiYGK+uYwMAAAqvIMeb+dT//zowWtuyZcsWc60YrX3RadZVqlQRf6JTs3VWk7ZXe3fgHyKHLvJ1E+DH9o2M9XUTAFh0/s5zz4xe+0Wv9KtXAf7Xv/51Me0EAAC49FOztSh369atF//OAAAAvrrOzL333mtuNQAAAGBlAfBff/0l7777rixfvtzcMynr/Zj0fkoAAAB+F2b27NkjkZGR8v3337svdrdz506PbXSaNgAAgF+GGb3Cr96HaeXKle7bF0yYMMHcLwkAAMDva2ayzuJevHixuRowAACAVQXALl5eogYAAMA3YUbrYbLWxFAjAwAArKmZ0Z6YXr16uW8mmZaWJo888sg5s5nmz5+fv60EAADIjzDTs2fPc643AwAAYE2YmTZtWsG1BAAA4FIXAAMAAPgaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKsRZgAAQOBMzQaASyFy6KJcb7tvZGyBtgWA/6NnBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABW82mYmTJlijRp0kRCQ0PNEhUVJYsXL3Y/n5aWJv369ZOKFStKmTJlpEuXLpKSkuLLJgMAAD/j0zBTrVo1GTlypCQlJcnGjRulTZs20rFjR9m+fbt5ftCgQfLZZ5/JvHnzZNWqVXLw4EHp3LmzL5sMAAD8TJDjOI74kQoVKsirr74qd955p1SqVElmz55tvlc//fST1K9fXxITE6V58+a5er3jx49LWFiYpKammt4f2HdXZOB8uGs2UDjl5fztNzUzZ8+elTlz5sjJkyfNcJP21pw5c0aio6Pd29SrV09q1KhhwkxO0tPTzQ7IvAAAgMLL52Fm27Ztph4mJCREHnnkEVmwYIE0aNBADh8+LMWLF5dy5cp5bB8eHm6ey0l8fLxJcq6levXql+C3AAAAARtm6tatK999952sX79eHn30UenZs6f88MMPXr9eXFyc6ZJyLcnJyfnaXgAA4F+K+boB2vtSu3Zt833Tpk1lw4YNMn78eOnataucPn1ajh075tE7o7OZIiIicnw97eHRBQAABAaf98xklZGRYepeNNgEBwdLQkKC+7kdO3bIgQMHTE0NAACAz3tmdEioffv2pqj3xIkTZubSV199JUuXLjX1Ln369JHBgwebGU5aydy/f38TZHI7kwkAABR+Pg0zR44ckfvvv18OHTpkwoteQE+DTLt27czzY8eOlSJFipiL5WlvTUxMjEyePNmXTQYAAH7G764zk9+4zox/4jozyC9cZwYonKy8zgwAAIA3CDMAAMBqPp+aDQCXasiSISmgcKJnBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGA1wgwAALAaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKsRZgAAgNUIMwAAwGqEGQAAYDXCDAAAsFoxXzcA/i1y6KJcb7tvZGyBtgW4WBzPQOFEzwwAALAaYQYAAFiNMAMAAKzm05qZ+Ph4mT9/vvz0009SsmRJadGihYwaNUrq1q3r3iYtLU2efPJJmTNnjqSnp0tMTIxMnjxZwsPDfdl0XGQ9AgAAhaJnZtWqVdKvXz9Zt26dLFu2TM6cOSO33nqrnDx50r3NoEGD5LPPPpN58+aZ7Q8ePCidO3f2ZbMBAIAf8WnPzJIlSzweT58+XSpXrixJSUnyt7/9TVJTU+Wdd96R2bNnS5s2bcw206ZNk/r165sA1Lx5cx+1HAAA+Au/qpnR8KIqVKhgvmqo0d6a6Oho9zb16tWTGjVqSGJiYravoUNRx48f91gAAEDh5TdhJiMjQwYOHCgtW7aURo0amXWHDx+W4sWLS7ly5Ty21XoZfS6nOpywsDD3Ur169UvSfgAAEOBhRmtnvv/+e1PoezHi4uJMD49rSU5Ozrc2AgAA/+MXVwB+/PHH5fPPP5fVq1dLtWrV3OsjIiLk9OnTcuzYMY/emZSUFPNcdkJCQswCAAACg097ZhzHMUFmwYIFsmLFCqlVq5bH802bNpXg4GBJSEhwr9uxY4ccOHBAoqKifNBiAADgb4r5emhJZyp98sknUrZsWXcdjNa66HVn9GufPn1k8ODBpig4NDRU+vfvb4IMM5kAAIDPw8yUKVPM11tuucVjvU6/7tWrl/l+7NixUqRIEenSpYvHRfMAAAB8HmZ0mOlCSpQoIZMmTTILAACA385mAgAA8AZhBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVivm6AQDgjyKHLsrT9vtGxhZYWwCcHz0zAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGA1wgwAALAaYQYAAFiNMAMAAKxGmAEAAFYjzAAAAKv5NMysXr1aOnToIFWrVpWgoCBZuHChx/OO48jzzz8vVapUkZIlS0p0dLT8/PPPPmsvAADwPz4NMydPnpSrr75aJk2alO3zo0ePlgkTJsjUqVNl/fr1Urp0aYmJiZG0tLRL3lYAAOCfivnyzdu3b2+W7GivzLhx4+TZZ5+Vjh07mnUzZ86U8PBw04PTrVu3S9xaAADgj/y2Zmbv3r1y+PBhM7TkEhYWJs2aNZPExMQcfy49PV2OHz/usQAAgMLLb8OMBhmlPTGZ6WPXc9mJj483oce1VK9evcDbCgAAfMdvw4y34uLiJDU11b0kJyf7ukkAACAQw0xERIT5mpKS4rFeH7uey05ISIiEhoZ6LAAAoPDy2zBTq1YtE1oSEhLc67T+RWc1RUVF+bRtAADAf/h0NtOff/4pu3bt8ij6/e6776RChQpSo0YNGThwoIwYMULq1Kljws1zzz1nrknTqVMnXzbbepFDF/m6CQAAFI4ws3HjRmndurX78eDBg83Xnj17yvTp02XIkCHmWjQPP/ywHDt2TFq1aiVLliyREiVK+LDVAADAnwQ5ekGXQkyHpnRWkxYDUz/zf+iZAfLfvpGx7FbAR+dvv62ZAQAAyA3CDAAAsJpPa2YAoLAoqOFbhq+AC6NnBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA1QgzAADAaoQZAABgNcIMAACwGmEGAABYjTADAACsRpgBAABW495MABCg94jivk8oLOiZAQAAViPMAAAAqxFmAACA1aiZCbAxcgAACht6ZgAAgNUIMwAAwGqEGQAAYDVqZi4halsA8P8NIP/RMwMAAKxGmAEAAFYjzAAAAKtRM3MRqIEBAMD36JkBAABWI8wAAACrEWYAAIDVrAgzkyZNksjISClRooQ0a9ZMvv32W183CQAA+Am/LwD+8MMPZfDgwTJ16lQTZMaNGycxMTGyY8cOqVy5sq+bBwDWsnESw76Rsb5uQkCIzMOx4Q+fid/3zIwZM0YeeugheeCBB6RBgwYm1JQqVUreffddXzcNAAD4Ab8OM6dPn5akpCSJjo52rytSpIh5nJiY6NO2AQAA/+DXw0z/+c9/5OzZsxIeHu6xXh//9NNP2f5Menq6WVxSU1PN1+PHj+d7+zLST+X7awIAclYQ/y/HxZ3fCuozcb2u4zh2hxlvxMfHy/Dhw89ZX716dZ+0BwCQf8LGsTcD7TM5ceKEhIWF2RtmLrvsMilatKikpKR4rNfHERER2f5MXFycKRh2ycjIkN9//10qVqwoQUFBBZYeNSwlJydLaGhogbxHYcM+Y59xjPkf/l2yz/zpONMeGQ0yVatWveBr+nWYKV68uDRt2lQSEhKkU6dO7nCijx9//PFsfyYkJMQsmZUrV+6StFc/FMIM+4zjzL/w75J9xnFm77/NC/XIWBFmlPay9OzZU66//nq58cYbzdTskydPmtlNAAAAfh9munbtKkePHpXnn39eDh8+LNdcc40sWbLknKJgAAAQmPw+zCgdUsppWMkf6LDWsGHDzhneAvuM48x3+HfJPuM4C5x/m0FObuY8AQAA+Cm/vmgeAADAhRBmAACA1QgzAADAaoQZAABgNcJMLqxevVo6dOhgrkKoVxFeuHDhBX/mq6++kuuuu85Ua9euXVumT58ugSKv+0v3lW6XddGp+IFCb8Nxww03SNmyZaVy5crmIpE7duy44M/NmzdP6tWrJyVKlJDGjRvLF198IYHAm/2l/wazHmO63wLFlClTpEmTJu4LlUVFRcnixYvP+zOBenx5u88C/RjLauTIkWYfDBw4UAr6OCPM5IJepO/qq6+WSZMm5Wqn7t27V2JjY6V169by3XffmQ/ywQcflKVLl0ogyOv+ctGT0aFDh9yLnqQCxapVq6Rfv36ybt06WbZsmZw5c0ZuvfVWsy9zsnbtWunevbv06dNHNm/ebE7ounz//fdS2Hmzv5SekDIfY/v375dAUa1aNXNySUpKko0bN0qbNm2kY8eOsn379my3D+Tjy9t9FujHWGYbNmyQN99804TB88m340ynZiP3dJctWLDgvNsMGTLEadiwoce6rl27OjExMQG3q3Ozv1auXGm2++OPPy5Zu/zdkSNHzD5ZtWpVjtvcfffdTmxsrMe6Zs2aOX379nUCTW7217Rp05ywsLBL2i5/V758eeftt9/O9jmOr7zvM46x/3PixAmnTp06zrJly5ybb77ZGTBggJOT/DrO6JkpAImJiRIdHe2xLiYmxqxHzvTqzlWqVJF27drJmjVrAnpXpaammq8VKlTIcRuOs7ztL/Xnn39KzZo1zU3uLvQXdmF29uxZmTNnjunJ0qGT7HB85X2fKY4xMb2mOjqR9TxYkMeZFVcAto3WemS93YI+1juF/ve//5WSJUv6rG3+SAPM1KlTzf230tPT5e2335ZbbrlF1q9fb+qOAo3eTFWHJlu2bCmNGjXK83EWSLVGedlfdevWlXfffdd0e2v4ee2116RFixYm0OhwQiDYtm2bORGnpaVJmTJlZMGCBdKgQYNst+X4yvs+4xgTE/g2bdpkhplyI7+OM8IMfE7/B6CLi55gdu/eLWPHjpX33ntPAvGvGh0v/uabb3zdlEK1v/SElPkvaj3O6tevb8b1X3rpJQkE+u9M6/g0zH300UfmJr5af5TTyRl522eBfowlJyfLgAEDTB3bpS58JswUgIiICElJSfFYp4+1MIxemdzRO6QH4slc70H2+eefmxlhF+otyOk40/WBIi/7K6vg4GC59tprZdeuXRIoihcvbmZXqqZNm5q/nsePH29OtllxfOV9nwX6MZaUlCRHjhzx6FHX4Tn99zlx4kTT8160aNECOc6omSkAmswTEhI81mlSPd84KzzpX0I6/BQotFZaT8zahb1ixQqpVavWBX8mkI8zb/ZXVvo/WR1CCKTjLLshOj3BZCeQjy9v91mgH2Nt27Y1v6/+/9u1aPlAjx49zPdZg0y+Hmd5KhcO4MrszZs3m0V32ZgxY8z3+/fvN88PHTrUue+++9zb79mzxylVqpTz9NNPOz/++KMzadIkp2jRos6SJUucQJDX/TV27Fhn4cKFzs8//+xs27bNVL4XKVLEWb58uRMoHn30UTPT5quvvnIOHTrkXk6dOuXeRveZ7juXNWvWOMWKFXNee+01c5wNGzbMCQ4ONvuwsPNmfw0fPtxZunSps3v3bicpKcnp1q2bU6JECWf79u1OINB9obO99u7d62zdutU8DgoKcr788kvzPMfXxe+zQD/GspN1NlNBHWeEmVxwTR3OuvTs2dM8r1/1A8v6M9dcc41TvHhx54orrjBT9gJFXvfXqFGjnCuvvNL8o69QoYJzyy23OCtWrHACSXb7S5fMx43uM9c+dJk7d65z1VVXmeNMLwewaNEiJxB4s78GDhzo1KhRw+yr8PBw5/bbb3c2bdrkBIrevXs7NWvWNL9/pUqVnLZt27pPyorj6+L3WaAfY7kJMwV1nAXpfy62awkAAMBXqJkBAABWI8wAAACrEWYAAIDVCDMAAMBqhBkAAGA1wgwAALAaYQYAAFiNMAPA7wUFBcnChQt93QwAfoowA0COHj0qjz76qNSoUUNCQkLMTd5iYmJkzZo17B0Afo+7ZgOQLl26yOnTp2XGjBlyxRVXmLvW6s3ffvvtN/YOAL9HzwwQ4I4dOyZff/21jBo1Slq3bi01a9aUG2+8UeLi4uQf//iHe7sxY8ZI48aNpXTp0lK9enV57LHH5M8//3Q/P336dClXrpx8/vnnUrduXSlVqpTceeedcurUKROSIiMjpXz58vLEE0+Yuwm76PqXXnpJunfvbl778ssvl0mTJp23zcnJyXL33Xeb96tQoYJ07NhR9u3bl+P2X331lRmqWrp0qVx77bVSsmRJadOmjRw5ckQWL14s9evXl9DQULnnnntMezPfITk+Pt7clVt/5uqrr5aPPvrI/bz+Hn369HE/r7/3+PHjPd67V69e0qlTJ3nttdfM3ZMrVqwo/fr1kzNnzuThUwJwPoQZIMCVKVPGLFqTkp6enuN2RYoUkQkTJsj27dtNOFmxYoUMGTLEYxsNArrNnDlzZMmSJSZE3HHHHfLFF1+Y5b333pM333zTIxCoV1991QSFzZs3y9ChQ2XAgAGybNmybNuhIUCHwMqWLWtCmA6Faftvu+0207t0Pi+88IJMnDhR1q5d6w5E48aNk9mzZ8uiRYvkyy+/lDfeeMO9vQaZmTNnytSpU83vPWjQILn33ntl1apV7rBTrVo1mTdvnvzwww/y/PPPyz//+U+ZO3eux/uuXLlSdu/ebb7qvtPgpwuAfJLnW1MCKHQ++ugjp3z58ubO5S1atHDi4uKcLVu2nPdn5s2b51SsWNH9WO9Yrf9L2bVrl3td3759nVKlSjknTpxwr4uJiTHrXfSuxLfddpvHa3ft2tVp3769+7G+7oIFC8z37733nlO3bl0nIyPD/Xx6erpTsmRJZ+nSpee9k/vy5cvd6+Lj48263bt3e7RX26fS0tJM29euXevxWn369HG6d++e437p16+f06VLF/djvUOw/o5//fWXe91dd91lfkcA+YOeGQCmZubgwYPy6aefmh4O7VG57rrrPHoPli9fLm3btjXDQNorct9995mamszDMjq0dOWVV7ofh4eHm2Ek7TnJvE6HdzKLioo65/GPP/6Y7SezZcsW2bVrl2mDq1dJh5rS0tJM78f5NGnSxKMd2l6tEcqubfoe+ru1a9fO/T66aE9N5vfRIbGmTZtKpUqVzPP//ve/5cCBAx7v27BhQylatKj7sQ43Zd0HALxHATAAo0SJEubErctzzz0nDz74oAwbNszUfGg9yt///ncz4+nll1824eGbb74x9SI6tKOhQAUHB3vsTa1TyW6dDs94S+t0NDy8//775zyngeJ8MrflQm1z1QPp8JMGuMx0xpfS4bSnnnpKXn/9dRPANGDpkNn69etzfN+s7wPg4hFmAGSrQYMG7mu7JCUlmZOvnrS1dkZlrQu5GOvWrTvnsRblZkd7jD788EOpXLmyKdotyN9fQ4v2stx8883ZbqP1Oi1atDDF0C4X6h0CkP8YZgICnA4V6cyeWbNmydatW2Xv3r2moHX06NFmlpCqXbu2KbzV4tg9e/aYQl4tis0vGgr0/Xbu3GmGbfT9tQg4Oz169JDLLrvMtE0LgLW9Oiyms6R++eWXfGuT9rJor4sW/WrRroaUTZs2mX2gj1WdOnVk48aNZpaUtl17tDZs2JBvbQCQO/TMAAFO6zyaNWsmY8eONSdsDS069fqhhx4yM3OUzjTSqdk6fVunbP/tb38zM33uv//+fGnDk08+aULB8OHDTW+LvpfOWMqODmmtXr1annnmGencubOcOHHCDANpPU9+99TolHEdutLfVUOcTgXXniHXfunbt6+ZgdW1a1czdKTTy7WXRqd7A7h0grQK+BK+HwB40ALhgQMHmgUAvMEwEwAAsBphBgAAWI1hJgAAYDV6ZgAAgNUIMwAAwGqEGQAAYDXCDAAAsBphBgAAWI0wAwAArEaYAQAAViPMAAAAqxFmAACA2Oz/AQEZQ1QSYtQoAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(10)\n",
    "\n",
    "population = np.random.exponential(scale=2.0, size=100000)\n",
    "\n",
    "sample_size = 30\n",
    "n_samples = 1000\n",
    "\n",
    "sample_means = []\n",
    "\n",
    "for i in range(n_samples):\n",
    "    sample = np.random.choice(population, size=sample_size, replace=True)\n",
    "    sample_means.append(sample.mean())\n",
    "\n",
    "plt.hist(population, bins=40)\n",
    "plt.title(\"Original population\")\n",
    "plt.xlabel(\"Value\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()\n",
    "\n",
    "plt.hist(sample_means, bins=40)\n",
    "plt.title(\"Distribution of sample means\")\n",
    "plt.xlabel(\"Sample mean\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e78d8f7",
   "metadata": {},
   "source": [
    "Even when the original data are not normally distributed, the distribution of sample means tends to become approximately normal when the sample size increases."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "411bd317",
   "metadata": {},
   "source": [
    "# Lab Example 2 — Confidence interval for a mean\n",
    "\n",
    "Objective: estimate a parameter with uncertainty.\n",
    "\n",
    "Use the repeated measurement example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "615beff5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 9.999333333333333\n",
      "Standard deviation: 0.04832430129073875\n",
      "95% confidence interval: 9.972572227269502 10.026094439397163\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "measurements = np.array([9.91, 10.03, 9.98, 10.05, 10.01, 9.96, 10.08, 9.94,\n",
    "                         10.02, 9.99, 10.04, 9.97, 10.06, 9.95, 10.00])\n",
    "\n",
    "n = len(measurements)\n",
    "xbar = measurements.mean()\n",
    "s = measurements.std(ddof=1)\n",
    "\n",
    "confidence = 0.95\n",
    "alpha = 1 - confidence\n",
    "\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df=n-1)\n",
    "margin_error = t_critical * s / np.sqrt(n)\n",
    "\n",
    "ci_lower = xbar - margin_error\n",
    "ci_upper = xbar + margin_error\n",
    "\n",
    "print(\"Mean:\", xbar)\n",
    "print(\"Standard deviation:\", s)\n",
    "print(\"95% confidence interval:\", ci_lower, ci_upper)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75ec3573",
   "metadata": {},
   "source": [
    "Interpretation:\n",
    "\n",
    "We do not report only the mean. We report the mean with an interval that reflects uncertainty.\n",
    "\n",
    "Suggested question:\n",
    "\n",
    "Does the confidence interval include 10\\,\\Omega?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2024490",
   "metadata": {},
   "source": [
    "# Lab Example 3 — Hypothesis test for a nominal value\n",
    "\n",
    "Objective: test whether the measured component is statistically consistent with a reference value.\n",
    "\n",
    "For the resistor example:\n",
    "\n",
    "H_0: \\mu = 10\n",
    "\n",
    "H_a: \\mu \\neq 10\n",
    "\n",
    "Python:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2fee9dc6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t statistic: -0.05343044448672866\n",
      "p-value: 0.9581438956150026\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "mu0 = 10.0\n",
    "\n",
    "t_statistic, p_value = stats.ttest_1samp(measurements, popmean=mu0)\n",
    "\n",
    "print(\"t statistic:\", t_statistic)\n",
    "print(\"p-value:\", p_value)"
   ]
  }
 ],
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