lab-sessions-26a/9-confident-hypothesis/main.ipynb

{
 "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": 2,
   "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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",
      "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": 4,
   "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": 7,
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "365d78c7",
   "metadata": {},
   "source": [
    "If p-value < 0.05, reject H0.\n",
    "If p-value >= 0.05, do not reject H0.\n",
    "\n",
    "A hypothesis test does not prove that the true resistance is exactly 10\\,\\Omega. It only evaluates whether the observed difference is large compared with random variation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cc4f360",
   "metadata": {},
   "source": [
    "# Lab Example 4 — Comparing two measurement methods\n",
    "\n",
    "Objective: connect with engineering experiments.\n",
    "\n",
    "Two instruments measure the same nominal resistor. Determine whether their mean readings are different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3cf2b671",
   "metadata": {},
   "outputs": [],
   "source": [
    "method_A = np.array([10.01, 9.98, 10.03, 9.97, 10.02, 10.00, 10.04, 9.99])\n",
    "method_B = np.array([10.08, 10.05, 10.07, 10.03, 10.06, 10.09, 10.04, 10.08])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0379e400",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t statistic: -5.019011475427952\n",
      "p-value: 0.0001995796758233766\n"
     ]
    }
   ],
   "source": [
    "t_statistic, p_value = stats.ttest_ind(method_A, method_B, equal_var=False)\n",
    "\n",
    "print(\"t statistic:\", t_statistic)\n",
    "print(\"p-value:\", p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a5ddea29",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/0c/2g7zyqyd3lj21c3yr8x3168m0000gn/T/ipykernel_3163/4104677222.py:1: MatplotlibDeprecationWarning: The 'labels' parameter of boxplot() has been renamed 'tick_labels' since Matplotlib 3.9; support for the old name will be dropped in 3.11.\n",
      "  plt.boxplot([method_A, method_B], labels=[\"Method A\", \"Method B\"])\n"
     ]
    },
    {
     "data": {
      "image/png": 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ij1mbErSz9JYtW+T1118362hI0yY37Xyqx6Fnz54mYGqY1NqtoUOHeuUY6OMcNWqU+ZLSx6jNVfpLWZurGjRoYOaJyQw6w/pXX31laiD19aGBQMOFzhGkcxxpCNJ5bFL6/Oj8Vhp8dH2tJdD19DHq86BzIymdB+qOO+4wx0MDlc7Jo/PcWGEsJR555BHTL0U7RGvNlJ5OR0OWnqZFl2vg0y/r9NIvY+1TpbWNWm59nWg/GA1ner9as/T111+ner96nPW1qMdUA7vW7lgdxDPis0H7junx1udT3+PaMV1rLrXpuX///mYuL6tc2iSqAzj0danvGa21SanUvJ+mTp1qXif6utCO5vpaeOutt8xxdg2j+qNPb9MaKX0daU2jrqcBy7UGHJkoE0bOAammw7X79etn5hzRYeWFChVyNG3a1MyDc/nyZed6//77r5kLRYcq58mTx8wRo0OcXddROtxWh/7a6VvCPnxeh0br8ldffdW5TIcy65DmQ4cOOeetKVWqlBkS7TrcXX3wwQdmSLUOyQ4JCTHDwa2h0ze6b9fbrGHsOhxZ5wCqU6eOOQ5aDv2/pzmLFi9ebIbr630XLVrU8fDDDzv++OMPt3Wsx2LnqYxJ0WH9+tj0mOtxeOqpp9zmhknLMH9PZdLh8TqfjJ2n5/PixYvmudc5rPQ1o/Pg6FxKr732mtuw8pQ8PzpnkE43ofMv6b70rw5Ht08joK8HnQ9K96XHQedg+uGHHzwO8/f0OJSWTee10tt1P7fccouZbkFf1zr1RWpfq67D2ZcsWeK2XOfZ0rmNdLi+3pcex27dupnHe6PnzdO0Bjrlgs4NpdMx6G3JDflPqkzWfrds2eK2PKlyLF261BEREWFeL3rR51CPy759+5zrxMbGmnmVihQp4jbcPqkyWMdRy5La95NVJp06QNfT+ai++OILcyxch/l//vnn5rNDpw/Q15TOXzVgwADHX3/9leQxw83lp/9kZkADsiKtldCaCE/NEwCArI8+SAAAADYEJAAAABsCEgAAgA19kAAAAGyoQQIAALAhIAEAANgwUWQa6bTweiZ1nZjsZk6vDwAA0k5nN9IJd3Uy0+RONk1ASiMNR/YTRwIAgKzh+PHjZhbzpBCQ0khrjqwDrNPyAwAA33fhwgVTwWF9jyeFgJRGVrOahiMCEgAAWcuNusfQSRsAAMCGgAQAAGBDQAIAALAhIAEAANgQkAAAAGwISAAAADYEJAAAAAISAABA8qhBAgAAsCEgAQAA2BCQAAAAbAhIAAAANpysFgCQbcXFxUlUVFSy68THx0t0dLQEBwdLYGBgsuuGhIRI/vz5vVxK+CICEgAg29JwFB4e7rX9RUZGSlhYmNf2B99FQAIAZFta46OhJjl79+6VXr16yaJFiyQ0NPSG+0POQEACAGRb2hyW0hofDUfUDsFCJ20AAAAbAhIAAIANAQkAAMCGgAQAAGBDQAIAACAgAQAAJI8aJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAAC+FJDWrVsnHTp0kLJly4qfn58sX77c7XaHwyFjx46VMmXKSGBgoLRu3VoOHDhww/3OmjVLgoODJV++fNKoUSPZvHmz2+0nT56URx55REqXLi0FChSQsLAwWbp0qdcfHwAAyJoyNSBdunRJ6tSpYwKNJ9OmTZOZM2fK7NmzZdOmTSbMtGnTRi5fvpzkPhcvXizDhg2TcePGybZt28z+dZvTp08713n00Udl37598tVXX8nOnTulS5cu0q1bN9m+fXuGPE4AAJC1+Dm0msYHaA3SsmXLpFOnTua6Fktrlp577jl5/vnnzbKYmBgpVaqUzJs3T3r06OFxP1pj1KBBA3n77bfN9YSEBKlQoYIMHjxYRo4caZYVLFhQ3n33XVOLZClWrJi88sor0rdvX4/7vXLlirlYLly4YParZSpcuLAXjwQAICW0ReHixYvpPlh79+6VXr16yaJFiyQ0NDTd+ytUqJBUq1Yt3ftBxtDv76CgoBt+f+cWH3XkyBHTFKbNahZ9QBqANm7c6DEgXb16VSIjI2XUqFHOZbly5TL70G0sTZo0MTVN7du3lyJFishnn31maqVatGiRZHmmTp0qEyZM8OpjBACkPRzddtttXj18GpK8Zf/+/YSkLM5nA5KGI6U1Rq70unWb3dmzZ+X69eset4mKinJe10DUvXt3U2uUO3duyZ8/v6m9qlq1apLl0dClTXf2GiQAwM1n1Rx5o9YnPj5eoqOjTd9V7e/qjdoob9RsIXP5bEDKSGPGjJHz58/Ljz/+KMWLFzedw7UP0vr166VWrVoetwkICDAXAIDv0HCkA23Sq2nTpl4pD7IPnw1IOsJMnTp1yoxis+j1unXretxGw46/v79Zx5Vet/Z36NAh0z9p165dcvvtt5tl2pFbw5F2FtcO4QAAIGfz2XmQKleubELNqlWr3Jq1dDRb48aNPW6TN29eCQ8Pd9tGO2nrdWubuLg4Z98kVxqsdF0AAIBMrUGKjY2VgwcPunXM3rFjhxQtWlQqVqwoQ4YMkUmTJpmObhqYtGlMR7ZZI91Uq1atpHPnzjJo0CBzXfsJ9e7dW+rXry8NGzaUGTNmmOkE+vTpY24PCQkxfY0GDBggr732mumHpE1sP/zwg3zzzTeZcBQAAICvydSAtHXrVmnZsqXzutUJWgOODuUfMWKECTf9+/c3fYYiIiJk5cqVZgJIizaZaedsi3a+PnPmjJlgUjtza3OcbmN13M6TJ498++23Zsi/TlKpIU0D0/z586Vdu3Y39fEDAADf5DPzIGXXeRQAAN6nEwFrlwqd2sUbnbSze7mQ+u9vn+2DBAAAkFkISAAAADYEJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAAA2BCQAAAAbAhIAAIANAQkAAMCGgAQAAGBDQAIAALAhIAEAANgQkAAAAGwISAAAADYEJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbHLbFwAAkBWULugngef3i5zwnd/6Wh4tF7I+AhIAIEsaEJ5XQtcNEFknPiP0f8uFrI+ABADIkt6LvCrdx86T0JAQ8RV7o6LkvdcfkvszuyBINwISACBLOhnrkPgit4mUrSu+Iv5kgikXsj7fabgFAADwEQQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAAB8KSCtW7dOOnToIGXLlhU/Pz9Zvny52+0Oh0PGjh0rZcqUkcDAQGndurUcOHDghvudNWuWBAcHS758+aRRo0ayefPmROts3LhR7rrrLilQoIAULlxYmjVrJvHx8V59fAAAIGvK1IB06dIlqVOnjgk0nkybNk1mzpwps2fPlk2bNpkw06ZNG7l8+XKS+1y8eLEMGzZMxo0bJ9u2bTP7121Onz7tFo7uvfdeueeee0x42rJliwwaNEhy5aJCDQAAZPKpRtq2bWsunmjt0YwZM+TFF1+Ujh07mmULFiyQUqVKmZqmHj16eNxu+vTp0q9fP+nTp4+5ruFqxYoVMnfuXBk5cqRZNnToUHnmmWec11X16tWTLeuVK1fMxXLhwoU0PGIAAJAV+GyVyZEjR+TkyZOmWc0SFBRkmsy0BsiTq1evSmRkpNs2Wiuk161ttCZJa6NKliwpTZo0MYGrefPm8vPPPydbnqlTp5r7ty4VKlTw2mMFAAC+xWcDkoYjpQHGlV63brM7e/asXL9+PdltDh8+bP6OHz/e1DStXLlSwsLCpFWrVsn2bxo1apTExMQ4L8ePH0/3YwQAAL4pU5vYMkNCQoL5O2DAAGczXL169WTVqlWmGU5rijwJCAgwFwAAkP35bA1S6dKlzd9Tp065Ldfr1m12xYsXF39//2S30RFxqkaNGm7rhIaGyrFjx7z6GAAAQNbkswGpcuXKJtRozY5rx2jtP9S4cWOP2+TNm1fCw8PdttEaI71ubaPD/3VagX379rltu3//fqlUqVKGPR4AAJB1ZGoTW2xsrBw8eNCtY/aOHTukaNGiUrFiRRkyZIhMmjRJqlWrZgLTmDFjTLjp1KmTcxvtO9S5c2czTF/pEP/evXtL/fr1pWHDhmYknE4nYDWn6XxLw4cPN9MA6BQAdevWlfnz50tUVJR8/vnnmXAUAACAr8nUgLR161Zp2bKl87qGG6UBZ968eTJixAgTbvr37y/nz5+XiIgI06laJ4C0HDp0yHTOtnTv3l3OnDljJpjUjtkagHQb147bGrx0LiUd7n/u3DkTlH744Qe59dZbb9pjBwAAvsvPoRMOIdW0uU+H++uINp2JGwBw8+hEwNqlQqd20ZHIvsJXy4XUf3/7bB8kAACAzEJAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAAA2BCQAAAAbAhIAAIBNbkmBLl26SGrNnj1bSpYsmertAAAAskRAWr58uXTr1k0CAwNTtNOPP/5YYmNjCUgAACD7BiQ1c+bMFAeezz//PD1lAgAA8P0+SKtXr5aiRYumeKf//e9/pVy5cukpFwAAgG/XIDVv3jxVO42IiEhreQAAALLeKLZt27bJzp07nde//PJL6dSpk7zwwgty9epVb5cPAADA9wPSgAEDZP/+/eb/hw8flh49ekj+/PllyZIlMmLEiIwoIwAAgG8HJA1HdevWNf/XUNSsWTMzam3evHmydOnSjCgjAACAbwckh8MhCQkJ5v8//vijtGvXzvy/QoUKcvbsWe+XEAAAwNcDUv369WXSpEmycOFCWbt2rbRv394sP3LkiJQqVSojyggAAODbAWnGjBmmo/agQYNk9OjRUrVqVefcR02aNMmIMgIAAPjmRJGW2rVru41is7z66qvi7+/vrXIBAJCkuLg481d/sKdXfHy8REdHS3BwcIrPGJGUvXv3prs8yKIByZWeTsTqj2TJkydPessEAECyoqKizN9+/fr55JEqVKhQZhcBNzsgaV8jbV5bs2aNXL582a3ztp+fn1y/fj29ZQIAIFk6/54KCQkxU82kt9anV69esmjRIgkNDfVKOKpWrVq694MsFpD0RaRhaO7cuaZTtoYiAABupuLFi0vfvn29uk8NR2FhYV7dJ3JQQPrtt98kMjJSqlevnjElAgAAyGqj2Bo0aCDHjx/PmNIAAABkxRqkOXPmyJNPPil//vmn1KxZM1GnbB3lBgAAkKMC0pkzZ+TQoUPSp08f5zLth0QnbQAAkGMD0uOPPy716tWTTz75hE7aAAAgW0p1QDp69Kh89dVXzhm0AQAAJKd30r7rrrvMSDYAAIDsKtU1SB06dJChQ4ea043UqlUrUSft+++/35vlAwAA8P2ApCPY1MSJExPdxkzaAAAgRwYk+7nXAAAAJKf3QQIAAMjuUl2DpFatWmUup0+fTlSjpOdoAwAAyFEBacKECab/Uf369aVMmTKcrBYAAGQ7qQ5Is2fPlnnz5skjjzySMSUCAADIan2Qrl69Kk2aNMmY0gAAAGTFgNS3b1/5+OOPvXLn69atM/MqlS1b1jTVLV++3O12Pb/b2LFjTVNeYGCgtG7dWg4cOHDD/c6aNUuCg4MlX7580qhRI9m8ebPH9XT/bdu29XjfAAAg50pRE9uwYcOc/9dO2f/5z3/kxx9/lNq1ayeaKHL69OkpvvNLly5JnTp1zPndunTpkuj2adOmycyZM2X+/PlSuXJlGTNmjLRp00b27Nljwo8nixcvNuXVpkANRzNmzDDb7Nu3T0qWLOm2rt6m4QgAACDVAWn79u1u1+vWrWv+7tq1y215asOG1t7oJanaHQ0wL774onTs2NEsW7BggTlBrtb29OjRw+N2GtD69esnffr0Mdc1KK1YscKMrhs5cqRzvR07dsjrr78uW7duNTVUN3LlyhVzsVy4cCFVjxW+Ky4uTqKiopJdJz4+XqKjo03NpNZmJickJETy58/v5VICAHwuIK1evVputiNHjsjJkydNs5olKCjI1Apt3LjRY0DS/lGRkZEyatQo57JcuXKZfeg2rl+IDz30kGmKK126dIrKM3XqVDOCD9mPhqPw8HCv7U9fg2FhYV7bHwAgi8yDZPnjjz/M3/Lly4u3aThSWmPkSq9bt9mdPXtWrl+/7nEb1xoCPZecdjS3aqZSQkOXa1Oj1iBVqFAhxdvDd2mNj4aa5Ozdu1d69eolixYtktDQ0BvuDwCQA081MmnSJNM8FRsba5YVKlRInnvuORk9erSpsfFlX331lfz000+Jmg1vJCAgwFyQ/WhzWEprfDQcUTsEANlfqtOMhqC3335bXn75ZRMy9DJlyhR56623TCdqb7Gavk6dOuW2XK8n1SxWvHhx8ff3T3YbDUeHDh2SIkWKSO7cuc1Fde3aVVq0aOG18gMAgBwUkHRE2Zw5c+Spp54yo9j08vTTT8v7779vJpD0Fh21pqFGT2ni2qy1adMmady4scdt8ubNa/qSuG6jNV563dpGO2r//vvvppO2dVFvvPGGfPjhh14rPwAAyEFNbOfOnfPYx0KX6W2poU10Bw8edOuYrYGlaNGiUrFiRRkyZIhpzqtWrZpzmL/OmdSpUyfnNq1atZLOnTvLoEGDzHXtJ9S7d29zKpSGDRuakXA6nYA1qk1Dl6caKL0/vQ8AAIBUBySdt0ib2HR+Ile6TG9LDR1i37JlS+d1qxO0BhytjRoxYoQJN/3795fz589LRESErFy50m0OJG0u087Zlu7du8uZM2fMBJPamVunJNBt7B23AQAAkuLn0AmHUmHt2rXSvn17U+NiNVvpEPrjx4/Lt99+K3feeafkBNrcp9MOxMTESOHChTO7OMhg27ZtM823DOEHsh/e3znLhRR+f6e6D1Lz5s1l//79pllLa3X0orNg60zVOSUcAQCA7C1N8yBpP6DJkyd7vzQAAAA+IEU1SDrqS0eDpdTu3bvl2rVr6SkXAACAbwekevXqyd9//53inWrfpGPHjqWnXAAAAL7dxKb9uHWIfUpPwKnnRAMAAMjWAalZs2amE3ZqapBudMZzAACALB2Q1qxZk/ElAQAA8BG+fWZZAACATEBAAgAAsCEgAQAA2BCQAAAAbAhIAAAA3ghICxculKZNm5pTjhw9etQsmzFjhnz55Zdp2R0AAEDWDkjvvvuuDBs2TNq1a2dOVHv9+nWzvEiRIiYkAQAA5LiA9NZbb8n7778vo0ePFn9/f+fy+vXry86dO71dPgAAAN8PSEeOHDHnZrMLCAiQS5cueatcAAAAWScgVa5cWXbs2JFo+cqVKyU0NNRb5QIAAPDtU4240v5HAwcOlMuXL5uT2G7evFk++eQTmTp1qsyZMydjSgkAAODLAalv377mRLQvvviixMXFyUMPPWRGs7355pvSo0ePjCklAACALwck9fDDD5uLBqTY2FgpWbKk90sGAEA66fdUVFRUsuvs3bvX7W9yQkJCJH/+/DwvOUDutHTSvnbtmlSrVs28SKwXyoEDByRPnjwSHBycEeUEACDVNByFh4enaN1evXrdcJ3IyEgJCwvjmcgBUh2QHnvsMXn88cdNQHK1adMm0wdpzZo13iwfAABppjU+GmqSEx8fL9HR0eYHvnYhudH+kDOkOiBt377dzKJtd8cdd8igQYO8VS4AANJNWzlSUuPj6XsNOVuqh/n7+fnJxYsXEy2PiYlxzqoNAACQowJSs2bNzJB+1zCk/9dlERER3i4fAACA7zexvfLKKyYkVa9eXe68806zbP369XLhwgX56aefMqKMAAAAvl2DVKNGDfn999+lW7ducvr0adPc9uijj5qRAjVr1syYUgIAAPj6PEg6MeSUKVO8XxoAAICsGpDOnz9vTjGiNUgJCQlut2ltEgAAQI4KSF9//bWZRVtn0C5cuLAZ1WbR/xOQAABAjuuD9Nxzz5mJIjUgaU3SP//847ycO3cuY0oJAADgywHpzz//lGeeeYZz0QAAgGwr1QGpTZs2snXr1owpDQAAQFbsg9S+fXsZPny47NmzR2rVqmVOUOvq/vvv92b5AAAAfD8g9evXz/ydOHFiotu0kzanGwEAADkuINmH9QMAAEhO74MEAACQ3aVposhLly7J2rVr5dixY3L16lW323SEGwAAQI4KSNu3b5d27dpJXFycCUpFixaVs2fPmmH/JUuWJCABAICc18Q2dOhQ6dChg5kYMjAwUH799Vc5evSohIeHy2uvvZYxpQQAAPDlGqQdO3bIe++9J7ly5RJ/f3+5cuWKVKlSRaZNmya9e/eWLl26ZExJgTQ4cOCAXLx4Md3Hbu/evW5/06tQoUJSrVo1r+wLAOADAUnnPdJwpLRJTfshhYaGSlBQkBw/fjwDigikPRzddtttXj18vXr18tq+9u/fT0gCgOwSkOrVqydbtmwxH+zNmzeXsWPHmj5ICxculJo1a2ZMKYE0sGqOFi1aZEJ8esTHx0t0dLQEBwebpuX00FooDVreqNkCAPhIQJoyZYrzg33y5Mny6KOPylNPPWUC0wcffJARZQTSRcNRWFhYuo9i06ZNeSYAIIdIdUCqX7++8//axLZy5UpvlwkAACBrjWK766675Pz584mWX7hwwdyWGuvWrTMj4sqWLWtOU7J8+XK32x0Oh2nCK1OmjGnWaN26telXciOzZs0yTSH58uWTRo0ayebNm523nTt3TgYPHizVq1c3+6xYsaKZmiAmJiZVZQcAANlXqgPSmjVrEk0OqS5fvizr169P1b50HqU6deqYQOOJjoybOXOmzJ49WzZt2iQFChSQNm3amPtKyuLFi2XYsGEybtw42bZtm9m/bnP69Glz+4kTJ8xFpyTYtWuXzJs3z9SCPfHEE6kqOwAAyL5S3MT2+++/O/+/Z88eOXnypPO6nqBWQ0a5cuVSdedt27Y1F0+09mjGjBny4osvSseOHc2yBQsWSKlSpUxNU48ePTxuN336dHNC3T59+pjrGq5WrFghc+fOlZEjR5qO5EuXLnWuf+utt5q+VNpp9tq1a5I7t+dDotMZ6MW1xgwAAOTwgFS3bl3TDKYXT01p2lz11ltvea1gR44cMSFMm9UsOpWANplt3LjRY0DSmq3IyEgZNWqUc5lOSaD70G2Sos1rhQsXTjIcqalTp8qECRPS9ZgAAEA2C0gaWLRWRyeF1D49JUqUcN6WN29e02FbJ470FquGSmuMXOl119orVzrdgNZmedomKioqyW1eeukl6d+/f7Ll0dClTXeuNUgVKlRI8eMBAADZMCBVqlTJ/E1ISJDsQkNO+/btpUaNGjJ+/Phk1w0ICDAXAACQ/aW6k/b8+fNNnx7LiBEjpEiRItKkSRNzTjZvKV26tPl76tQpt+V63brNrnjx4qYWKyXb6FxO9957rznlw7Jly8wM4QAAAGkKSDpRpDWTsPbrefvtt81oMw0neiJbb6lcubIJNatWrXKr8dHRbI0bN/a4jTb16UlzXbfRGi+97rqN7ueee+4x63/11VdmOgAAAIA0TxSp51urWrWq+b+OJnvggQdM/x2dZbhFixap2ldsbKwcPHjQrZ+Tngy3aNGiZn6iIUOGyKRJk8ws3RqYxowZY+ZM6tSpk3ObVq1aSefOnWXQoEHmuvYT0pPm6oSWDRs2NCPhdDoBa1SbFY7i4uLMKSj0ujUiTftVebMfFQAAyCEBqWDBgvL333+bAPP99987Oy5rLYyeryo1tm7dKi1btnRet/alAUfnJ9LmOw03GsB0csqIiAgznYBrjc+hQ4dMR2tL9+7d5cyZM2aCSe3MraPvdBur47bOjaS1UMoKeq4BTSeYBAAAOVuqA9Ldd98tffv2NSet1bORt2vXzizfvXt3qsOF1jjpyLik6JQCEydONJek6AlE7bQ2yapRSu19AgAApLoPks56rf15tJZGJ1wsVqyYWa7zD/Xs2ZMjCgAAcl4Nko5Y047ZdkyiCAAAclRA0tOM6Ck6dFZq11OOeFK7dm1vlQ0AAMB3A5J2dNYOzzpbtnXKEdd+PNZ1/aszWQMAAGT7gKSju6xTi+j/AQAAJKcHJOs0I/b/AwAAZEc+e6oRAACAzOKzpxoBAADIkacaAQAAyBY1SNapRpSeakRn1k7rqUYAAAB8UaaeagQAAMAXcaoRAAAAG041AgAAkN4aJLV+/Xrp1auXGdr/559/mmULFy6Un3/+OS27AwAAyNoBaenSpdKmTRsz1H/btm1y5coVszwmJsZMAQAAAJDjAtKkSZNk9uzZ8v7770uePHmcy3WYvwYmAACAHBeQ9u3bJ82aNUu0PCgoSM6fP++tcgEAAGSdgFS6dGk5ePBgouXa/6hKlSreKhcAAEDWCUj9+vWTZ599VjZt2iR+fn5y4sQJ+eijj+T555+Xp556KmNKCQAA4MvD/EeOHCkJCQnSqlUriYuLM81tAQEBJiANHjw4Y0oJAADgywFJa41Gjx4tw4cPN01tsbGxUqNGDXMKEj3ViHUiWwAAgBw1D5LKmzevCUYNGzY0o9mmT58ulStX9m7pAAAAfDkg6XxHo0aNkvr165sJIpcvX26Wf/jhhyYYvfHGGzJ06NCMLCsAAIBvNbGNHTtW3nvvPWndurVs2LBBHnzwQenTp4/8+uuvpvZIr/v7+2dsaQEAAHwpIC1ZskQWLFgg999/v+zatUtq164t165dk99++830SwIAAMhxTWx//PGHhIeHm//XrFnTjFzTJjXCEQAAyLEB6fr166ZjtiV37txm5BoAAECObWJzOBzy2GOPmZojdfnyZXnyySelQIECbut98cUX3i8lAACALwak3r17u13v1atXRpQHAAAg6wQkHc4PAACQE6R5okgAAIDsioAEAABgQ0ACAABI78lqgaykdEE/CTy/X+SE7/wW0PJouQAAvouAhGxtQHheCV03QGSd+IzQ/y0XAMB3EZCQrb0XeVW6j50noSEh4iv2RkXJe68/JPdndkEAAEkiICFbOxnrkPgit4mUrSu+Iv5kgikXAMB3+U7HDAAAAB9BQAIAALAhIAEAANgQkAAAAGwISAAAADYEJAAAABsCEgAAgA0BCQAAwJcC0rp166RDhw5StmxZ8fPzk+XLl7vd7nA4ZOzYsVKmTBkJDAyU1q1by4EDB26431mzZklwcLDky5dPGjVqJJs3b3a7/fLlyzJw4EApVqyYFCxYULp27SqnTp3y+uMDAABZU6YGpEuXLkmdOnVMoPFk2rRpMnPmTJk9e7Zs2rRJChQoIG3atDEBJymLFy+WYcOGybhx42Tbtm1m/7rN6dOnnesMHTpUvv76a1myZImsXbtWTpw4IV26dMmQxwgAALIgh4/Qoixbtsx5PSEhwVG6dGnHq6++6lx2/vx5R0BAgOOTTz5Jcj8NGzZ0DBw40Hn9+vXrjrJlyzqmTp3q3EeePHkcS5Ysca6zd+9ec/8bN25Mcr+XL192xMTEOC/Hjx832+j/4ZsiIyPNc6R/fYmvlgsAcoKYmJgUfX/7bB+kI0eOyMmTJ02zmiUoKMg0mW3cuNHjNlevXpXIyEi3bXLlymWuW9vo7f/++6/bOiEhIVKxYsUk96umTp1q7t+6VKhQwUuPFAAA+BqfDUgajlSpUqXclut16za7s2fPyvXr15PdRv/mzZtXihQpkuL9qlGjRklMTIzzcvz48TQ/NgAA4NtyZ3YBsoqAgABzAQAA2Z/P1iCVLl3a/LWPLtPr1m12xYsXF39//2S30b/aFHf+/PkU7xcAAOQsPhuQKleubALLqlWrnMsuXLhgRrM1btzY4zbadBYeHu62TUJCgrlubaO358mTx22dffv2ybFjx5LcLwAAyFkytYktNjZWDh486NYxe8eOHVK0aFHTaXrIkCEyadIkqVatmglMY8aMMXMmderUyblNq1atpHPnzjJo0CBzXYf49+7dW+rXry8NGzaUGTNmmOkE+vTpY27XDtZPPPGEWU/vp3DhwjJ48GATju64445MOAoAAMDXZGpA2rp1q7Rs2dJ5XUOL0oAzb948GTFihAk3/fv3N01iERERsnLlSjMBpOXQoUOmc7ale/fucubMGTPBpHa6rlu3rtnGteP2G2+8YUa36QSRV65cMfMkvfPOOzftcQMAAN/mp2P9M7sQWZE292ltlI5o01oo+B6dKFSbVHVqh7CwMPEVvlouAMgJLqTw+9tn+yABAABkFgISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAAA2BCQAAAAbAhIAAIANAQkAAMCGgAQAAGBDQAIAALAhIAEAANgQkAAAAGwISAAAADYEJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACATW77AiC7iIuLM3+3bduW7n3Fx8dLdHS0BAcHS2BgYLr2tXfv3nSXBwCQsQhIyLaioqLM3379+okvKlSoUGYXAQCQBAISsq1OnTqZvyEhIZI/f/501/r06tVLFi1aJKGhoV4JR9WqVUv3fgAAGYOAhGyrePHi0rdvX6/uU8NRWFiYV/cJAPA9dNIGAACwISABAADYEJAAAABsCEgAAAA2BCQAAAAbAhIAAIANAQkAAMCGgAQAAGBDQAIAALAhIAEAANgQkAAAAGwISAAAADYEJAAAABsCEgAAgA0BCQAAIKsFpIsXL8qQIUOkUqVKEhgYKE2aNJEtW7Yku82sWbMkNDTUrF+9enVZsGBBonVmzJhhbtN1KlSoIEOHDpXLly9n4CMBAABZRW7xcX379pVdu3bJwoULpWzZsrJo0SJp3bq17NmzR8qVK5do/XfffVdGjRol77//vjRo0EA2b94s/fr1k1tuuUU6dOhg1vn4449l5MiRMnfuXBO49u/fL4899pj4+fnJ9OnTM+FRAgAAX+LTASk+Pl6WLl0qX375pTRr1swsGz9+vHz99dcmCE2aNCnRNhqkBgwYIN27dzfXq1SpYmqcXnnlFWdA2rBhgzRt2lQeeughcz04OFh69uwpmzZtSrIsV65cMRfLhQsXvP54AQCAb/DpJrZr167J9evXJV++fG7LtVns559/9riNhhhP62tN0r///muua61RZGSkWaYOHz4s3377rbRr1y7JskydOlWCgoKcF22WAwAA2ZNPB6RChQpJ48aN5aWXXpITJ06YsKRNbBs3bpS//vrL4zZt2rSROXPmmADkcDhk69at5rqGo7Nnz5p1tOZo4sSJEhERIXny5JFbb71VWrRoIS+88EKSZdFmu5iYGOfl+PHjGfa4AQBA5vLpgGQ1mWnQ0f5GAQEBMnPmTNMcliuX56KPGTNG2rZtK3fccYcJPx07dpTevXub26xt1qxZI1OmTJF33nlHtm3bJl988YWsWLHCBLGk6H0XLlzY7QIAALInnw9IWruzdu1aiY2NNbU2VlOZ9i3yRJvTtPN1XFycREdHy7Fjx0wfI62NKlGihDNEPfLII6YDeK1ataRz584mMGkzWkJCwk1+hAAAwNf4fECyFChQQMqUKSP//POPfPfdd6ZmKDlae1S+fHnx9/eXTz/9VO677z5nDZKGJ3sNlK6ntLYKAADkbD49ik1pGNLQonMWHTx4UIYPHy4hISHSp08fZ9+gP//80znXkQ7Z11qmRo0amTClw/Z1moD58+c796mj2XR5vXr1zHq6X61V0uVWUAIAADmXzwck7RCtIeiPP/6QokWLSteuXWXy5MmmhkhpZ21tRrNoR+7XX39d9u3bZ9Zp2bKlGdavzWyWF1980cx5pH81XGnTm4Yj3S8AAICfgzalNNF5kHS4vwY4Omxnf9qZPzw83IyODAsLy+ziAAAy+Ps7y/RBAgAAuFkISAAAADYEJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAAA2BCQAAACb3PYFQE4TFxcnUVFRya6zd+9et7/JCQkJkfz583utfACAm4+AhBxPw1F4eHiKjkOvXr1uuE5kZKSEhYXl+OMKAFkZAQk5ntb4aKhJTnx8vERHR0twcLAEBgbecH8AgKzNz+FwODK7EFnRhQsXJCgoSGJiYqRw4cKZXRwAAODF7286aQMAANgQkAAAAGwISAAAADYEJAAAABsCEgAAgA0BCQAAwIaABAAAYENAAgAAsCEgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACATW77AqSMw+FwnhUYAABkDdb3tvU9nhQCUhpdvHjR/K1QoUJadwEAADLxezwoKCjJ2/0cN4pQ8CghIUFOnDghhQoVEj8/P45SDvjFoWH4+PHjUrhw4cwuDgAv4v2dszgcDhOOypYtK7lyJd3TiBqkNNKDWr58+bRujixKwxEBCcieeH/nHEHJ1BxZ6KQNAABgQ0ACAACwISABKRAQECDjxo0zfwFkL7y/4QmdtAEAAGyoQQIAALAhIAEAANgQkAAAAGwISAAAADYEJMCmRYsWMmTIEK8fl/Hjx0vdunU53kAm4v2NlCIgIct47LHHzGldnnzyyUS3DRw40Nym66TUmjVrzDbnz58XX9OmTRvx9/eXLVu2ZHZRgJsiu7+/o6OjTXmsS968eaVq1aoyadKkG540FZmDgIQsRc+H9umnn0p8fLxz2eXLl+Xjjz+WihUrSnZw7Ngx2bBhgwwaNEjmzp2b2cUBbpqc8P7+8ccf5a+//pIDBw7IhAkTZPLkybzPfRQBCVlKWFiY+RD94osvnMv0//rhWa9evUQnFJ46dapUrlxZAgMDpU6dOvL55587f821bNnS/P+WW25J9OtUtx0xYoQULVpUSpcubZrH7CGmY8eOUrBgQXP+pm7dusmpU6fc1nn55ZelVKlS5oTGTzzxhPmgT4kPP/xQ7rvvPnnqqafkk08+cfuyALKznPD+LlasmLnPSpUqycMPPyxNmzaVbdu2peFoIaMRkJDlPP744yZEWLSWpU+fPonW0w/PBQsWyOzZs2X37t0ydOhQ6dWrl6xdu9Z8CC9dutSst2/fPvOL7s0333RuO3/+fClQoIBs2rRJpk2bJhMnTpQffvjB+eGqH57nzp0z+9Llhw8flu7duzu3/+yzz8yH7pQpU2Tr1q1SpkwZeeedd2742LSqXR+bljMkJMRUwVsf+kBOkJ3f33a6bWRkpDRq1CjV2+ImcABZRO/evR0dO3Z0nD592hEQEOCIjo42l3z58jnOnDljbtN11OXLlx358+d3bNiwwW0fTzzxhKNnz57m/6tXr9aGf8c///zjtk7z5s0dERERbssaNGjg+J//+R/z/++//97h7+/vOHbsmPP23bt3m31t3rzZXG/cuLHj6aefdttHo0aNHHXq1En2Meq+S5Qo4fj333/N9TfeeMOUB8jusvv7+8iRI2YfgYGBjgIFCjjy5Mljrvfv3z+NRwwZLffNCGGAN5UoUULat28v8+bNMzUu+v/ixYu7rXPw4EGJi4uTu+++22351atXE1XVe1K7dm236/oL8fTp0+b/e/fuNb9Q9WKpUaOGFClSxNzWoEED89fe2bRx48ayevXqZO9Xfy3rL9Xcuf//W7Nnz54yfPhwOXTokNx66603LDeQ1WXn97davHixhIaGyr///iu7du2SwYMHm2ZAbbKDbyEgIctWw2snZjVr1qxEt8fGxpq/K1askHLlyrndlpITzubJk8ftuvZh0Kr3jKRV+suWLTMfnO+++65z+fXr101w0s6cQE6QHd/fFg1e2nSuNCjpj58xY8aYJrt8+fLdlDIgZeiDhCzp3nvvNb8WNUzokHg7/cWnH5Ta2VI/jFwv1i9DHWZrBZDU0A+148ePm4tlz549Zjix3q+1jvZvcPXrr78mu9+PPvpIypcvL7/99pvs2LHDeXn99dfNr+nUlhPIqrLj+zspOp3HtWvXzOOFb6EGCVmSfqhoNbf1fzsdWfL888+bjpv6yzAiIkJiYmLkl19+MaNSevfubUaR6C/Hb775Rtq1a2dGwuiolRtp3bq11KpVy4xAmTFjhvlwe/rpp6V58+ZSv359s86zzz5rRs3odR2louFHO5JWqVIlyf1+8MEH8sADD0jNmjXdlusH/qhRo2TlypWmuQHI7rLj+9vy999/y8mTJ81+d+7caTqP64g7LTd8CzVIyLL0AyW5D5WXXnrJVF3raBf9xae/SrVKXocFK62a13lIRo4caYbrWlX6N6Iful9++aXpN9CsWTPzgaofjNq3wKL9iPS+dShxeHi4HD161AzbT4qOZNGao65duya6LSgoSFq1amUCFJBTZKf3tyvdn/Z5Cg4Olv79+5vw5rpv+A4/7amd2YUAAADwJdQgAQAA2BCQAAAAbAhIAAAANgQkAAAAGwISAACADQEJAADAhoAEAABgQ0ACAACwISABAADYEJAAAABsCEgAAADi7v8Bavw9LY00LWUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot([method_A, method_B], labels=[\"Method A\", \"Method B\"])\n",
    "plt.ylabel(\"Resistance [ohms]\")\n",
    "plt.title(\"Comparison of measurement methods\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bb81aef",
   "metadata": {},
   "source": [
    "Assuming the test was:\n",
    "\n",
    "$H_0$: $\\mu_A = \\mu_B$\n",
    "\n",
    "$H_a$: $\\mu_A \\neq \\mu_B$\n",
    "\n",
    "and using:\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "then:\n",
    "\n",
    "$p = 0.0001996 < 0.05$\n",
    "\n",
    "Therefore, you reject $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6490f025",
   "metadata": {},
   "source": [
    "At the 5% significance level, the two-sample t-test provides sufficient evidence to conclude that the mean measurements obtained with Method A and Method B are different. Since the test statistic is negative, Method A has a lower sample mean than Method B.\n",
    "\n",
    "This result may suggest that the two instruments or methods are not equivalent. The difference could be due to:\n",
    "\n",
    "* calibration offset,\n",
    "* systematic bias,\n",
    "* different sensor accuracy,\n",
    "* different measurement procedure,\n",
    "* environmental or operator effects."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d06cc2f",
   "metadata": {},
   "source": [
    "# Lab Example 5 — Bootstrap confidence interval\n",
    "\n",
    "Objective: show computational inference without relying only on formulas.\n",
    "\n",
    "Use the same measurement dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c4179929",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap 95% CI: [ 9.976      10.02268333]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(10)\n",
    "\n",
    "B = 5000\n",
    "bootstrap_means = []\n",
    "\n",
    "for i in range(B):\n",
    "    bootstrap_sample = np.random.choice(measurements, size=n, replace=True)\n",
    "    bootstrap_means.append(bootstrap_sample.mean())\n",
    "\n",
    "bootstrap_means = np.array(bootstrap_means)\n",
    "\n",
    "ci_bootstrap = np.percentile(bootstrap_means, [2.5, 97.5])\n",
    "\n",
    "print(\"Bootstrap 95% CI:\", ci_bootstrap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5ca91c65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(bootstrap_means, bins=40)\n",
    "plt.axvline(ci_bootstrap[0], linestyle=\"--\")\n",
    "plt.axvline(ci_bootstrap[1], linestyle=\"--\")\n",
    "plt.xlabel(\"Bootstrap mean\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.title(\"Bootstrap distribution of the mean\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "52a1d044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original mean: 12.2\n",
      "95% bootstrap CI: 11.77 12.620000000000001\n"
     ]
    }
   ],
   "source": [
    "#Lab Example 7 — Bootstrap confidence interval for the mean\n",
    "\n",
    "#Goal: connect directly with your previous lab.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "data = np.array([12.1, 11.8, 10.9, 13.0, 12.5, 11.7, 12.9, 13.2, 11.5, 12.4])\n",
    "\n",
    "B = 5000\n",
    "bootstrap_means = []\n",
    "\n",
    "for _ in range(B):\n",
    "    sample_boot = np.random.choice(data, size=len(data), replace=True)\n",
    "    bootstrap_means.append(np.mean(sample_boot))\n",
    "\n",
    "bootstrap_means = np.array(bootstrap_means)\n",
    "\n",
    "ci_low, ci_high = np.percentile(bootstrap_means, [2.5, 97.5])\n",
    "\n",
    "plt.hist(bootstrap_means, bins=30, edgecolor=\"black\")\n",
    "plt.axvline(ci_low, linestyle=\"--\", label=\"2.5%\")\n",
    "plt.axvline(ci_high, linestyle=\"--\", label=\"97.5%\")\n",
    "plt.axvline(data.mean(), linestyle=\"-\", label=\"Original mean\")\n",
    "plt.xlabel(\"Bootstrap means\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.title(\"Bootstrap distribution of the mean\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print(\"Original mean:\", data.mean())\n",
    "print(\"95% bootstrap CI:\", ci_low, ci_high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4d7d77da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True beta_0: 3\n",
      "Estimated beta_0: 3.717585051473372\n",
      "True beta_1: 2\n",
      "Estimated beta_1: 1.6815735189709737\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "n = 40\n",
    "beta_0 = 3\n",
    "beta_1 = 2\n",
    "sigma = 4\n",
    "\n",
    "x = np.linspace(0, 10, n)\n",
    "error = np.random.normal(0, sigma, n)\n",
    "y = beta_0 + beta_1 * x + error\n",
    "\n",
    "X = np.column_stack((np.ones(n), x))\n",
    "\n",
    "beta_hat = np.linalg.inv(X.T @ X) @ X.T @ y\n",
    "\n",
    "b0_hat, b1_hat = beta_hat\n",
    "\n",
    "y_hat = b0_hat + b1_hat * x\n",
    "\n",
    "plt.scatter(x, y, label=\"Data\")\n",
    "plt.plot(x, y_hat, label=\"OLS fitted line\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.title(\"OLS estimation\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print(\"True beta_0:\", beta_0)\n",
    "print(\"Estimated beta_0:\", b0_hat)\n",
    "print(\"True beta_1:\", beta_1)\n",
    "print(\"Estimated beta_1:\", b1_hat)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv (3.14.3)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}