{
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   "cell_type": "markdown",
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   "source": [
    "# Lab\n",
    "\n",
    "- Use this assignment to practice the chapter's concepts and coding skills in runnable Python code.\n",
    "- Sign in from the account menu before you start working on the assignment.\n",
    "- Write and run your code directly in the coding cells.\n",
    "- Multiple submissions are allowed. The highest score is kept.\n",
    "\n",
    "<div data-lab-answers-release-at=\"2099-12-31T23:59:00-06:00\"></div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Question 1: Delivery Percentiles\n",
    "# An online store wants to promise a delivery time that most orders meet.\n",
    "#   1. Compute the 75th and 90th percentiles of days with\n",
    "#      np.percentile(..., method='nearest'), as in this chapter.\n",
    "# These describe this sample, not a guaranteed future delivery promise.\n",
    "# Print exactly:\n",
    "# 75th percentile: 6\n",
    "# 90th percentile: 8\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "days = pd.Series([2, 3, 3, 4, 4, 5, 5, 6, 8, 12])\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "hide-input",
     "lab-answer"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "75th percentile: 6\n90th percentile: 8\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "days = pd.Series([2, 3, 3, 4, 4, 5, 5, 6, 8, 12])\n",
    "\n",
    "print(\"75th percentile:\", np.percentile(days, 75, method='nearest'))\n",
    "print(\"90th percentile:\", np.percentile(days, 90, method='nearest'))\n",
    "# Nine of these ten observed orders arrived within 8 days.\n",
    "# A small historical sample does not guarantee future delivery performance.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Question 2: An Estimate and One Resample\n",
    "# HR has a random sample of 12 salaries (in $1,000s) and wants to estimate the\n",
    "# median salary of all employees.\n",
    "#   1. Compute the sample median: the estimate of the population median.\n",
    "#   2. Draw len(salaries) values WITH replacement using salaries.sample(\n",
    "#      len(salaries), replace=True, random_state=3). Compute its median.\n",
    "# Print exactly:\n",
    "# Sample median: 71.0\n",
    "# Resample median: 84.5\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input",
     "lab-answer"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Sample median: 71.0\nResample median: 84.5\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "resample = salaries.sample(len(salaries), replace=True, random_state=3)\n",
    "\n",
    "print(\"Sample median:\", salaries.median())\n",
    "print(\"Resample median:\", resample.median())\n",
    "# Some salaries appear more than once in the resample and some\n",
    "# not at all, which is what drawing with replacement does.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Question 3: A 95% Bootstrap Confidence Interval\n",
    "# Generate a bootstrap distribution for the population median salary.\n",
    "#   1. Repeat 5,000 times: draw len(salaries) values with rng.choice(...,\n",
    "#      size=len(salaries), replace=True), and append np.median(resample)\n",
    "#      to bootstrap_medians. Initialize the list before your for loop.\n",
    "#   2. Use its 2.5th and 97.5th percentiles (method='nearest') as endpoints.\n",
    "# The seed is set once; do not reset it in the loop. The original sample\n",
    "# still contains only 12 employees, so interpret this interval cautiously.\n",
    "# Print exactly:\n",
    "# 95% CI: 63.0 to 84.5\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "rng = np.random.default_rng(42)\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "hide-input",
     "lab-answer"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "95% CI: 63.0 to 84.5\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "rng = np.random.default_rng(42)\n",
    "bootstrap_medians = []\n",
    "for i in range(5000):\n",
    "    resample = rng.choice(salaries, size=len(salaries), replace=True)\n",
    "    bootstrap_medians.append(np.median(resample))\n",
    "\n",
    "left = np.percentile(bootstrap_medians, 2.5, method='nearest')\n",
    "right = np.percentile(bootstrap_medians, 97.5, method='nearest')\n",
    "print(\"95% CI:\", left, \"to\", right)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Question 4: 95% vs. 80% Confidence\n",
    "# Using the same bootstrap medians:\n",
    "#   1. Compute the width of the 95% interval (2.5th to 97.5th percentile).\n",
    "#   2. Compute the width of the 80% interval (10th to 90th percentile).\n",
    "#   Use method='nearest' for all percentiles.\n",
    "# Print exactly:\n",
    "# 95% width: 21.5\n",
    "# 80% width: 13.0\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "rng = np.random.default_rng(42)\n",
    "bootstrap_medians = []\n",
    "for i in range(5000):\n",
    "    resample = rng.choice(salaries, size=len(salaries), replace=True)\n",
    "    bootstrap_medians.append(np.median(resample))\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "hide-input",
     "lab-answer"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "95% width: 21.5\n80% width: 13.0\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "salaries = pd.Series([62, 58, 75, 81, 66, 93, 70, 59, 88, 64, 120, 72])\n",
    "rng = np.random.default_rng(42)\n",
    "bootstrap_medians = []\n",
    "for i in range(5000):\n",
    "    resample = rng.choice(salaries, size=len(salaries), replace=True)\n",
    "    bootstrap_medians.append(np.median(resample))\n",
    "\n",
    "def width(low, high):\n",
    "    return np.percentile(bootstrap_medians, high, method='nearest') - np.percentile(bootstrap_medians, low, method='nearest')\n",
    "\n",
    "print(\"95% width:\", width(2.5, 97.5))\n",
    "print(\"80% width:\", width(10, 90))\n",
    "# Here the 80% interval is narrower; ties can produce equal widths.\n",
    "# More resamples alone would not add employees to the original sample.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Question 5: Is It a Majority?\n",
    "# In a random sample of 200 customers, 116 (0.58) would recommend the store.\n",
    "# The 40 supplied bootstrap proportions are a short arithmetic exercise.\n",
    "# Use thousands of resamples and check the sampling design before acting.\n",
    "#   1. Compute the 95% confidence interval (method='nearest').\n",
    "#   2. Check whether the whole interval is above 0.5, which supports the claim\n",
    "#      that a majority of all customers would recommend the store.\n",
    "# Print exactly:\n",
    "# 95% CI: 0.52 to 0.625\n",
    "# Whole interval above 0.5: True\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "bootstrap_props = pd.Series([0.585, 0.56, 0.585, 0.57, 0.595, 0.62, 0.56, 0.555, 0.53, 0.545,\n",
    "                             0.56, 0.625, 0.525, 0.59, 0.54, 0.585, 0.575, 0.565, 0.61, 0.585,\n",
    "                             0.59, 0.52, 0.575, 0.56, 0.615, 0.585, 0.52, 0.54, 0.58, 0.59,\n",
    "                             0.645, 0.58, 0.585, 0.575, 0.61, 0.565, 0.6, 0.58, 0.515, 0.565])\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "hide-input",
     "lab-answer"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "95% CI: 0.52 to 0.625\nWhole interval above 0.5: True\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "bootstrap_props = pd.Series([0.585, 0.56, 0.585, 0.57, 0.595, 0.62, 0.56, 0.555, 0.53, 0.545,\n",
    "                             0.56, 0.625, 0.525, 0.59, 0.54, 0.585, 0.575, 0.565, 0.61, 0.585,\n",
    "                             0.59, 0.52, 0.575, 0.56, 0.615, 0.585, 0.52, 0.54, 0.58, 0.59,\n",
    "                             0.645, 0.58, 0.585, 0.575, 0.61, 0.565, 0.6, 0.58, 0.515, 0.565])\n",
    "\n",
    "left = np.percentile(bootstrap_props, 2.5, method='nearest')\n",
    "right = np.percentile(bootstrap_props, 97.5, method='nearest')\n",
    "\n",
    "print(\"95% CI:\", left, \"to\", right)\n",
    "print(\"Whole interval above 0.5:\", left > 0.5)\n",
    "# This coarse practice interval supports, but does not prove, a majority.\n"
   ]
  },
  {
   "cell_type": "markdown",
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    "    <div class='ch11-lab-feedback-row' data-question='q4'><strong>Question 4</strong><span></span></div>\n",
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