{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8d46d378",
   "metadata": {},
   "source": [
    "# Sampling Variability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c22b1c1a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:09.332877Z",
     "iopub.status.busy": "2026-10-19T20:55:09.332591Z",
     "iopub.status.idle": "2026-10-19T20:55:10.604828Z",
     "shell.execute_reply": "2026-10-19T20:55:10.602984Z"
    },
    "tags": [
     "hide-input",
     "thebe-init",
     "runnable"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "sns.set_theme()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55359b74",
   "metadata": {},
   "source": [
    "```{contents}\n",
    ":local:\n",
    ":depth: 2\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "106a4597",
   "metadata": {},
   "source": [
    "In Section 8.1, we treated the 244 bills in the `tips` data as a **sample** from all the bills at a restaurant. A number computed from a sample, such as a sample mean or a sample proportion, is called a **statistic**. The number we really want, such as the mean of all bills, is a **parameter** of the population. Because a different sample would give a different statistic, every estimate carries some **uncertainty**. This section uses simulation to see how much statistics vary from sample to sample, and how sample size controls that variation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfb8b06b",
   "metadata": {},
   "source": [
    "## Samples from a Known Population\n",
    "\n",
    "In real analyses we never see the whole population. To watch sampling variability happen, we flip the situation around: we treat the 244 bills as the **entire population** and draw small random samples from them. Then we know the true answer and can compare each sample to it.\n",
    "\n",
    "The population mean is a **parameter**. We usually write it as $\\mu$ (mu)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eeb04b46",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:10.607941Z",
     "iopub.status.busy": "2026-10-19T20:55:10.607457Z",
     "iopub.status.idle": "2026-10-19T20:55:10.619475Z",
     "shell.execute_reply": "2026-10-19T20:55:10.618624Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population mean (mu): 19.79\n"
     ]
    }
   ],
   "source": [
    "tips = sns.load_dataset('tips')\n",
    "bills = tips['total_bill'].to_numpy()       ### the population: all 244 bills\n",
    "\n",
    "mu = bills.mean()                           ### parameter: population mean\n",
    "print('Population mean (mu):', round(mu, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "581395d9",
   "metadata": {},
   "source": [
    "Now draw a random sample of 20 bills and compute its mean. The **sample mean**, written $\\bar x$ (x-bar), is a **statistic**. We sample with replacement, as if each bill were drawn at random from the restaurant's steady stream of customers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ed61c0d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:10.621526Z",
     "iopub.status.busy": "2026-10-19T20:55:10.621340Z",
     "iopub.status.idle": "2026-10-19T20:55:10.626951Z",
     "shell.execute_reply": "2026-10-19T20:55:10.625673Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 1 mean: 22.45\n",
      "Sample 2 mean: 17.54\n",
      "Sample 3 mean: 20.98\n"
     ]
    }
   ],
   "source": [
    "rng = np.random.default_rng(42)\n",
    "n = 20\n",
    "\n",
    "for i in range(3):\n",
    "    sample = rng.choice(bills, size=n, replace=True)     ### one random sample of 20 bills\n",
    "    print(f'Sample {i + 1} mean: {sample.mean():.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2778a76a",
   "metadata": {},
   "source": [
    "Each sample gives a different mean, and none of them equals $\\mu$ exactly. That is **sampling variability**. To see its pattern, we repeat the process 5,000 times and plot all 5,000 sample means. The distribution of a statistic across repeated samples is called its **sampling distribution**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "02cd646b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:10.628969Z",
     "iopub.status.busy": "2026-10-19T20:55:10.628789Z",
     "iopub.status.idle": "2026-10-19T20:55:11.065332Z",
     "shell.execute_reply": "2026-10-19T20:55:11.064173Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of the sample means: 19.78\n",
      "SD of the sample means:   1.99\n"
     ]
    }
   ],
   "source": [
    "n_sims = 5_000\n",
    "sample_means = np.array([rng.choice(bills, size=n, replace=True).mean() for _ in range(n_sims)])\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(11, 4))\n",
    "sns.histplot(bills, bins=20, color=\"#bab0ac\", ax=ax[0])\n",
    "ax[0].axvline(mu, color=\"black\", linestyle=\":\", label=\"population mean\")\n",
    "ax[0].set(xlabel=\"total bill ($)\", title=\"Population: 244 bills\")\n",
    "ax[0].legend()\n",
    "\n",
    "sns.histplot(sample_means, bins=30, color=\"#4c78a8\", ax=ax[1])\n",
    "ax[1].axvline(mu, color=\"black\", linestyle=\":\", label=\"population mean\")\n",
    "ax[1].set(xlabel=\"sample mean ($)\", title=f\"5,000 sample means (n = {n})\")\n",
    "ax[1].legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print('Mean of the sample means:', round(sample_means.mean(), 2))\n",
    "print('SD of the sample means:  ', round(sample_means.std(ddof=1), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "622cf8ea",
   "metadata": {},
   "source": [
    "Three things stand out:\n",
    "\n",
    "- **Center**: the sample means are centered on the population mean. Any single sample can miss, but on average the sample mean hits the target.\n",
    "- **Spread**: the sample means vary much less than individual bills. Averaging 20 bills cancels out many of the high and low values.\n",
    "- **Shape**: the bills themselves are skewed to the right, but the sample means form a roughly symmetric, bell-shaped distribution. This is the **Central Limit Theorem** from Section 8.2, now applied to sample means.\n",
    "\n",
    "The SD of the sample means measures how far a sample mean typically lands from $\\mu$. It has its own name, the **standard error**, which we return to below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f422ec16",
   "metadata": {},
   "source": [
    "## Simulating Sample Proportions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46e9283d",
   "metadata": {},
   "source": [
    "The same idea works for proportions. Suppose 60% of a store's customers use a loyalty card. Each customer is like a flip of a weighted coin that comes up \"yes\" with probability $p = 0.6$. We simulate many samples of customers to see how the **sample proportion** varies.\n",
    "\n",
    "Key quantities:\n",
    "- True proportion $p$ (a parameter)\n",
    "- Sample size $n$\n",
    "- **Sample proportion** $\\hat p$ (a statistic)\n",
    "- **Sampling distribution**: distribution of $\\hat p$ across repeated samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3eab9a17",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.067394Z",
     "iopub.status.busy": "2026-10-19T20:55:11.067193Z",
     "iopub.status.idle": "2026-10-19T20:55:11.077437Z",
     "shell.execute_reply": "2026-10-19T20:55:11.076413Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    5000.000\n",
       "mean        0.600\n",
       "std         0.078\n",
       "min         0.350\n",
       "2.5%        0.450\n",
       "50%         0.600\n",
       "97.5%       0.750\n",
       "max         0.850\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.default_rng(seed=0)\n",
    "\n",
    "p_true = 0.6\n",
    "n = 40\n",
    "n_sims = 5_000\n",
    "\n",
    "# Draw many samples and compute sample proportions\n",
    "samples = rng.binomial(n=n, p=p_true, size=n_sims)      # Draw samples from a binomial distribution\n",
    "sample_props = samples / n                              # Compute sample proportions    \n",
    "\n",
    "summary = pd.Series(sample_props).describe(percentiles=[0.025, 0.5, 0.975]).round(3)\n",
    "summary\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26ea2de4",
   "metadata": {},
   "source": [
    "We see that \n",
    "\n",
    "- 97.5% of the simulated sample proportions fell at or below 0.750.\n",
    "- 2.5%, the lower bound, is 0.450.\n",
    "- the middle 95% of simulated proportions fall between 0.45 and 0.75.\n",
    "\n",
    "Now let us take a look at the sampling distribution: the distribution of sample proportions (`sample_props`) generated from 5,000 simulated samples."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfb8eb92",
   "metadata": {},
   "source": [
    "## Sampling Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d6d74f4e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.079466Z",
     "iopub.status.busy": "2026-10-19T20:55:11.079273Z",
     "iopub.status.idle": "2026-10-19T20:55:11.218378Z",
     "shell.execute_reply": "2026-10-19T20:55:11.217220Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 4))\n",
    "sns.histplot(sample_props, bins=15, stat=\"density\", color=\"#4c78a8\", edgecolor=\"white\", ax=ax)\n",
    "\n",
    "ax.axvline(sample_props.mean(), color=\"#f58518\", linestyle=\"--\", label=f\"mean = {sample_props.mean():.3f}\")\n",
    "ax.axvline(p_true, color=\"#54a24b\", linestyle=\":\", label=\"true p\")\n",
    "ax.set(xlabel=\"sample proportion\", ylabel=\"density\", title=\"Sampling distribution of p-hat (n=40, p=0.6)\")\n",
    "ax.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb8f674b",
   "metadata": {},
   "source": [
    "### Two Levels: the Data and the Samples\n",
    "\n",
    "It is easy to mix up two different distributions here:\n",
    "\n",
    "| | One survey's data | The sampling distribution |\n",
    "|---|---|---|\n",
    "| What is in it | 40 yes/no answers from one sample of customers | 5,000 values of $\\hat p$, one from each simulated survey |\n",
    "| Summarized by | one number, $\\hat p$ | its center and spread (the standard error) |\n",
    "| Where it comes from | what a company actually collects | imagined, or simulated |\n",
    "\n",
    "The histogram above shows the **sampling distribution**: each bar counts surveys, not customers. A company only ever runs one survey, so it sees one $\\hat p$. The sampling distribution tells it how far that one number might be from the truth."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f18f64d",
   "metadata": {},
   "source": [
    "## Standard Error"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fca11f6",
   "metadata": {},
   "source": [
    "For a sample proportion, the **standard error** measures the typical deviation of $\\hat p$ from $p$:\n",
    "\n",
    "$$\\text{SE}(\\hat p) = \\sqrt{\\dfrac{p(1-p)}{n}}$$\n",
    "\n",
    "The SE is \"sampling variability\" expressed as a single number: it is the standard deviation of the sampling distribution of $\\hat p$. Here $p = 0.6$ is the true proportion (a parameter), and $\\hat p$ is the proportion observed in one sample (a statistic).\n",
    "\n",
    "Note that:\n",
    "\n",
    "- $p(1-p)$ is the variance of a single yes/no observation. It is largest at $p = 0.5$ (most uncertain) and shrinks as $p$ approaches 0 or 1. For example, if $p = 0.6$, then $0.6 \\times 0.4 = 0.24$.\n",
    "- **Plug in $\\hat p$**: in real data analysis you don't know $p$ (that's why you're sampling!), so you substitute the observed $\\hat p$ into the formula. It's an approximation, but it works well for reasonably large $n$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90a7e4c4",
   "metadata": {},
   "source": [
    "Here we compare the empirical SD of simulations vs. the theoretical SE, to confirm that they match.\n",
    "In the comparison below, `ddof` stands for Delta Degrees of Freedom. It controls the denominator used in the std calculation. If ddof=0, divides by n (population std); if ddof=1, divides by n−1 (sample std).\n",
    "\n",
    "- The theoretical SE is the formula applied to the known values: \n",
    "\n",
    "    ```text\n",
    "    sqrt(0.6 × (1-0.6) / 40) ≈ 0.0775.\n",
    "    ```\n",
    "\n",
    "- The empirical SE is the standard deviation of the 5,000 simulated p-hat values -- no formula, purely from the simulation.\n",
    "\n",
    "- If the theoretical SE comes out nearly identical with the empirical (simulation) SE, then it validates that the formula is correct and the simulation is working as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "db72583c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.220619Z",
     "iopub.status.busy": "2026-10-19T20:55:11.220417Z",
     "iopub.status.idle": "2026-10-19T20:55:11.225572Z",
     "shell.execute_reply": "2026-10-19T20:55:11.224391Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical SE: 0.0775\n",
      "Simulated SE:   0.0781\n"
     ]
    }
   ],
   "source": [
    "se_theoretical = np.sqrt(p_true * (1 - p_true) / n)\n",
    "se_empirical = sample_props.std(ddof=1)\n",
    "\n",
    "print(f\"Theoretical SE: {se_theoretical:.4f}\")\n",
    "print(f\"Simulated SE:   {se_empirical:.4f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b094384c",
   "metadata": {},
   "source": [
    "### Margin of Error\n",
    "\n",
    "The sampling distribution of $\\hat p$ is roughly normal, so the 68–95–99.7 rule from Section 8.2 applies: about 95% of sample proportions land within **2 standard errors** of $p$. Two standard errors is the **margin of error**, the \"plus or minus\" reported with surveys and polls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "35789f2c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.227438Z",
     "iopub.status.busy": "2026-10-19T20:55:11.227252Z",
     "iopub.status.idle": "2026-10-19T20:55:11.232635Z",
     "shell.execute_reply": "2026-10-19T20:55:11.231350Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Margin of error (2 SE): 0.155\n",
      "p ± 2 SE: 0.445 to 0.755\n",
      "Simulated middle 95%: [0.45 0.75]\n"
     ]
    }
   ],
   "source": [
    "moe = 2 * se_theoretical\n",
    "print(f\"Margin of error (2 SE): {moe:.3f}\")\n",
    "print(f\"p ± 2 SE: {p_true - moe:.3f} to {p_true + moe:.3f}\")\n",
    "print(\"Simulated middle 95%:\", np.percentile(sample_props, [2.5, 97.5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c33d814",
   "metadata": {},
   "source": [
    "The range $0.6 \\pm 0.155$, or about 0.445 to 0.755, matches the middle 95% of the 5,000 simulated proportions (0.45 to 0.75).\n",
    "\n",
    "**Worked example.** In practice we do not know $p$. Suppose a survey of 40 customers finds that 26 would renew, so $\\hat p = 26/40 = 0.65$. Plugging in $\\hat p$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7b2c3add",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.234938Z",
     "iopub.status.busy": "2026-10-19T20:55:11.234733Z",
     "iopub.status.idle": "2026-10-19T20:55:11.239833Z",
     "shell.execute_reply": "2026-10-19T20:55:11.238742Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-hat: 0.65\n",
      "SE: 0.0754\n",
      "Plausible range for p: 0.50 to 0.80\n"
     ]
    }
   ],
   "source": [
    "p_hat = 26 / 40\n",
    "se_hat = np.sqrt(p_hat * (1 - p_hat) / 40)\n",
    "\n",
    "print(f\"p-hat: {p_hat:.2f}\")\n",
    "print(f\"SE: {se_hat:.4f}\")\n",
    "print(f\"Plausible range for p: {p_hat - 2 * se_hat:.2f} to {p_hat + 2 * se_hat:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0860bfb0",
   "metadata": {},
   "source": [
    "The true share of customers who would renew is plausibly anywhere from about 50% to 80%. A survey of 40 cannot tell a manager whether \"half\" or \"four out of five\" customers will renew. If the decision depends on that difference, the company needs a larger sample. Chapter 11 turns this idea into confidence intervals."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d402c03a",
   "metadata": {},
   "source": [
    "### SE of a Sample Mean\n",
    "\n",
    "The sample mean has a standard error formula too. If the population has standard deviation $\\sigma$ (sigma), the standard error of the mean of $n$ observations is\n",
    "\n",
    "$$\\text{SE}(\\bar x) = \\dfrac{\\sigma}{\\sqrt{n}}$$\n",
    "\n",
    "Let us check it against the tips simulation from the start of this section. Because the 244 bills are the whole population, we use the population SD, `np.std()` with its default `ddof=0`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3b0756e9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.242025Z",
     "iopub.status.busy": "2026-10-19T20:55:11.241832Z",
     "iopub.status.idle": "2026-10-19T20:55:11.247608Z",
     "shell.execute_reply": "2026-10-19T20:55:11.246458Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Population SD (sigma): 8.88\n",
      "SE formula, n = 20:    1.99\n",
      "Simulated SE:          1.99\n"
     ]
    }
   ],
   "source": [
    "sigma = np.std(bills)                                  ### population SD of the 244 bills\n",
    "se_mean_formula = sigma / np.sqrt(20)\n",
    "se_mean_sim = sample_means.std(ddof=1)                 ### SD of the 5,000 simulated sample means\n",
    "\n",
    "print(f\"Population SD (sigma): {sigma:.2f}\")\n",
    "print(f\"SE formula, n = 20:    {se_mean_formula:.2f}\")\n",
    "print(f\"Simulated SE:          {se_mean_sim:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13894dce",
   "metadata": {},
   "source": [
    "The formula and the simulation agree. Individual bills vary by about \\$8.88, but means of 20 bills vary by only about \\$2. As with proportions, in practice we do not know $\\sigma$, so we plug in the sample SD $s$ and use $s / \\sqrt{n}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d3dab7",
   "metadata": {},
   "source": [
    "## Effect of Sample Size"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56f47cc8",
   "metadata": {},
   "source": [
    "Larger samples shrink variability. Below we compare sampling distributions (p-hats) across different $n$ while keeping $p=0.6$ fixed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "313007de",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-19T20:55:11.249742Z",
     "iopub.status.busy": "2026-10-19T20:55:11.249523Z",
     "iopub.status.idle": "2026-10-19T20:55:11.409688Z",
     "shell.execute_reply": "2026-10-19T20:55:11.408515Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n</th>\n",
       "      <th>mean(p-hat)</th>\n",
       "      <th>sd(p-hat)</th>\n",
       "      <th>SE formula</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>0.5994</td>\n",
       "      <td>0.1549</td>\n",
       "      <td>0.1549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>40</td>\n",
       "      <td>0.5984</td>\n",
       "      <td>0.0780</td>\n",
       "      <td>0.0775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>200</td>\n",
       "      <td>0.5986</td>\n",
       "      <td>0.0348</td>\n",
       "      <td>0.0346</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     n  mean(p-hat)  sd(p-hat)  SE formula\n",
       "0   10       0.5994     0.1549      0.1549\n",
       "1   40       0.5984     0.0780      0.0775\n",
       "2  200       0.5986     0.0348      0.0346"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def simulate_props(n, p=0.6, sims=5_000):\n",
    "    props = rng.binomial(n=n, p=p, size=sims) / n   # Simulate sample proportions by drawing from a binomial distribution and dividing by n\n",
    "    return props\n",
    "\n",
    "ns = [10, 40, 200]\n",
    "records = []\n",
    "frames = []\n",
    "for n_i in ns:\n",
    "    props_i = simulate_props(n=n_i)\n",
    "    frames.append(pd.DataFrame({\"n\": n_i, \"prop\": props_i}))    # Store the sample proportions in a DataFrame for plotting\n",
    "    records.append({\n",
    "        \"n\": n_i,\n",
    "        \"mean(p-hat)\": props_i.mean(),\n",
    "        \"sd(p-hat)\": props_i.std(ddof=1),\n",
    "        \"SE formula\": np.sqrt(p_true * (1 - p_true) / n_i)\n",
    "    })\n",
    "\n",
    "display(pd.DataFrame(records).round(4))\n",
    "\n",
    "plot_df = pd.concat(frames, ignore_index=True)\n",
    "fig, ax = plt.subplots(figsize=(7, 4))\n",
    "sns.histplot(data=plot_df, x=\"prop\", hue=\"n\", element=\"step\", stat=\"density\", common_norm=False, palette=\"Dark2\", ax=ax)\n",
    "vline = ax.axvline(p_true, color=\"black\", linestyle=\":\")\n",
    "ax.set(xlabel=\"sample proportion\", title=\"Larger n reduces sampling variability\")\n",
    "\n",
    "leg = ax.get_legend()\n",
    "handles = list(leg.legend_handles) + [vline]\n",
    "labels = [t.get_text() for t in leg.get_texts()] + [\"true p\"]\n",
    "ax.legend(handles=handles, labels=labels, title=\"n\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ceff47e",
   "metadata": {},
   "source": [
    "```{admonition} Common mistakes\n",
    ":class: warning\n",
    "\n",
    "- **Confusing SD and SE.** The standard deviation describes how much *individual values* vary (single bills vary by about \\$8.88). The standard error describes how much an *estimate* varies from sample to sample (means of 20 bills vary by about \\$2). Use the SD to describe data and the SE to describe the precision of a statistic.\n",
    "- **Thinking a bigger sample fixes a biased one.** The standard error assumes a **random** sample. If a company surveys only customers who use its app, a sample of 10,000 gives a very precise estimate of the wrong thing. Sample size reduces chance error, not bias.\n",
    "- **Thinking a bigger population needs a bigger sample.** The SE formula depends on the sample size $n$, not on the size of the population. A random sample of 1,000 is about as precise for a city as for a whole country.\n",
    "- **The gambler's fallacy.** The law of large numbers does not mean that results \"even out\" in the short run. After five tails in a row, the next fair coin flip is still 50–50; the long-run average settles because later flips swamp the early ones, not because chance corrects itself.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d7b2edf",
   "metadata": {},
   "source": [
    "**Takeaways**\n",
    "- Repeated samples vary; summarizing their distribution clarifies how much.\n",
    "- Standard error captures typical sampling fluctuation and shrinks as $n$ grows.\n",
    "- Simulations help check formulas and build intuition about variability.\n",
    "\n",
    "As $n$ gets larger, the $\\hat p$ values from repeated samples cluster more tightly around the true $p$. In the plot, the histogram for $n = 200$ is much narrower than for $n = 10$: the same true $p = 0.6$, but larger samples give estimates that are consistently closer to it.\n",
    "\n",
    "The SE formula shows why: $\\text{SE} = \\sqrt{p(1-p)/n}$, so as $n$ increases, the SE decreases. Because $n$ is under a square root, quadrupling the sample size only cuts the SE in half. A larger sample gives you more information, so your estimate is less noisy. The SE turns the **uncertainty** in an estimate into a number a manager can use: a survey of 200 customers pins down the true proportion much more tightly than a survey of 10."
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    "\n",
    "## Section Practice\n",
    "\n",
    "Use this short exercise to check the main workflow from this section.\n"
   ]
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   "source": [
    "### Exercise: Practice Sampling Variability\n",
    "# About 30% of a bank's customers use mobile check deposit. The bank plans a survey.\n",
    "# The standard error of a sample proportion is sqrt(p * (1 - p) / n).\n",
    "#   1. Compute the standard error for samples of 100 and of 900 customers.\n",
    "#   2. How many times smaller is the standard error with 900 customers?\n",
    "#   3. Print the two standard errors (3 decimals) and the ratio (1 decimal).\n",
    "#   4. A survey of 100 customers finds that 27 of them use mobile deposit.\n",
    "#      Is 0.27 a parameter or a statistic? Store the word in `kind`.\n",
    "#   5. Deposit amounts have a standard deviation of $400. Compute the standard\n",
    "#      error of the mean deposit, sd / sqrt(n), for n = 100 and n = 400.\n",
    "# Print exactly:\n",
    "# SE with n=100: 0.046\n",
    "# SE with n=900: 0.015\n",
    "# Ratio: 3.0\n",
    "# 0.27 is a: statistic\n",
    "# SE of mean deposit, n=100: 40.0\n",
    "# SE of mean deposit, n=400: 20.0\n",
    "import numpy as np\n",
    "\n",
    "p = 0.3\n",
    "sd_deposit = 400\n",
    "### Your code starts here\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here"
   ]
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     "text": [
      "SE with n=100: 0.046\n",
      "SE with n=900: 0.015\n",
      "Ratio: 3.0\n",
      "0.27 is a: statistic\n",
      "SE of mean deposit, n=100: 40.0\n",
      "SE of mean deposit, n=400: 20.0\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "\n",
    "p = 0.3\n",
    "sd_deposit = 400\n",
    "\n",
    "se_100 = np.sqrt(p * (1 - p) / 100)\n",
    "se_900 = np.sqrt(p * (1 - p) / 900)\n",
    "\n",
    "print('SE with n=100:', round(se_100, 3))\n",
    "print('SE with n=900:', round(se_900, 3))\n",
    "print('Ratio:', round(se_100 / se_900, 1))\n",
    "# Nine times the sample size gives a standard error three times smaller,\n",
    "# because the standard error shrinks with the square root of n.\n",
    "\n",
    "kind = 'statistic'          # computed from a sample; the parameter is the true 30%\n",
    "print('0.27 is a:', kind)\n",
    "\n",
    "print('SE of mean deposit, n=100:', sd_deposit / np.sqrt(100))\n",
    "print('SE of mean deposit, n=400:', sd_deposit / np.sqrt(400))"
   ]
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