{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{div} assignment-question-card\n",
    "\n",
    "**1. A Valid Model?**\n",
    "\n",
    "A shipping team writes down this model for one delivery: on time with probability 0.80, 1 day late with probability 0.15, and 3 or more days late with probability 0.10. This is a valid probability model.\n",
    "\n",
    "<div class=\"tf-options\" role=\"radiogroup\" aria-label=\"Question 1 answer\">\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q1\" value=\"true\"> True</label>\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q1\" value=\"false\"> False</label>\n",
    "</div>\n",
    "\n",
    "::::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "### Solution\n",
    "# False\n",
    "# The probabilities add up to 1.05. In a valid model, the probabilities of all outcomes add up to exactly 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{div} assignment-question-card\n",
    "\n",
    "**2. Reading an Expected Value**\n",
    "\n",
    "The expected late-delivery credit is \\$1.75 per shipment. This means a typical shipment costs the store \\$1.75 in credits.\n",
    "\n",
    "<div class=\"tf-options\" role=\"radiogroup\" aria-label=\"Question 2 answer\">\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q2\" value=\"true\"> True</label>\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q2\" value=\"false\"> False</label>\n",
    "</div>\n",
    "\n",
    "::::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "### Solution\n",
    "# False\n",
    "# Each shipment costs $0, $5, or $20. The expected value is the long-run average credit over many shipments, not the cost of a typical one.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{div} assignment-question-card\n",
    "\n",
    "**3. Mean vs Median**\n",
    "\n",
    "A company pays most employees between \\$50,000 and \\$80,000, but a few executives earn over \\$1 million. The median salary describes a typical employee better than the mean salary does.\n",
    "\n",
    "<div class=\"tf-options\" role=\"radiogroup\" aria-label=\"Question 3 answer\">\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q3\" value=\"true\"> True</label>\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q3\" value=\"false\"> False</label>\n",
    "</div>\n",
    "\n",
    "::::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "### Solution\n",
    "# True\n",
    "# The few very large salaries pull the mean up. The median is the middle value, so it is not affected by how large the top salaries are.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{div} assignment-question-card\n",
    "\n",
    "**4. Two Surveys**\n",
    "\n",
    "A random sample of 100 customers shows 72% are satisfied. A second random sample of 100 customers, taken the same week, shows 68%. The difference shows that customer satisfaction changed.\n",
    "\n",
    "<div class=\"tf-options\" role=\"radiogroup\" aria-label=\"Question 4 answer\">\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q4\" value=\"true\"> True</label>\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q4\" value=\"false\"> False</label>\n",
    "</div>\n",
    "\n",
    "::::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "### Solution\n",
    "# False\n",
    "# Two random samples from the same population give different results by chance. That is sampling variability, not evidence of a change.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{div} assignment-question-card\n",
    "\n",
    "**5. Bigger Samples**\n",
    "\n",
    "If a manager surveys 400 customers instead of 100, the standard error of the sample proportion is cut in half.\n",
    "\n",
    "<div class=\"tf-options\" role=\"radiogroup\" aria-label=\"Question 5 answer\">\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q5\" value=\"true\"> True</label>\n",
    "  <label><input type=\"radio\" name=\"ch08-hw-q5\" value=\"false\"> False</label>\n",
    "</div>\n",
    "\n",
    "::::\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "### Solution\n",
    "# True\n",
    "# The standard error is proportional to 1 / sqrt(n). Four times the sample size gives half the standard error.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### 6. Return Rate\n",
    "# Each row of orders is one order. Use the data to estimate probabilities.\n",
    "#   1. Compute the proportion of orders that were returned.\n",
    "#   2. Use the complement to compute the proportion that were kept.\n",
    "# Print exactly:\n",
    "# Return rate: 0.15\n",
    "# Kept rate: 0.85\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "orders = pd.DataFrame({\n",
    "    \"returned\": [\"No\", \"No\", \"Yes\", \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\", \"No\",\n",
    "                 \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\", \"No\", \"No\", \"No\", \"No\"],\n",
    "})\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "hide-input",
     "homework-answer"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Return rate: 0.15\n",
      "Kept rate: 0.85\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "orders = pd.DataFrame({\n",
    "    \"returned\": [\"No\", \"No\", \"Yes\", \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\", \"No\",\n",
    "                 \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\", \"No\", \"No\", \"No\", \"No\"],\n",
    "})\n",
    "\n",
    "return_rate = (orders['returned'] == 'Yes').mean()\n",
    "\n",
    "print(\"Return rate:\", return_rate)\n",
    "print(\"Kept rate:\", round(1 - return_rate, 2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### 7. Items per Order\n",
    "# The warehouse recorded how many items were in each of 10 orders.\n",
    "#   1. Use value_counts(normalize=True) to get the empirical distribution of items.\n",
    "#   2. Print the proportion of orders with exactly 2 items.\n",
    "#   3. Print the average number of items per order.\n",
    "# Print exactly:\n",
    "# Proportion with 2 items: 0.4\n",
    "# Average items: 2.1\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "items = pd.Series([1, 2, 2, 3, 1, 2, 4, 2, 1, 3])\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "hide-input",
     "homework-answer"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion with 2 items: 0.4\n",
      "Average items: 2.1\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "items = pd.Series([1, 2, 2, 3, 1, 2, 4, 2, 1, 3])\n",
    "\n",
    "distribution = items.value_counts(normalize=True)\n",
    "\n",
    "print(\"Proportion with 2 items:\", distribution[2])\n",
    "print(\"Average items:\", items.mean())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### 8. Call Wait Times\n",
    "# A call center recorded wait times in minutes.\n",
    "#   1. Compute the median wait time.\n",
    "#   2. Compute the 90th percentile of wait times with np.percentile().\n",
    "# Print exactly:\n",
    "# Median wait: 4.5\n",
    "# 90th percentile: 12.1\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "waits = pd.Series([2, 3, 3, 4, 4, 5, 6, 7, 12, 13])\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input",
     "homework-answer"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median wait: 4.5\n",
      "90th percentile: 12.1\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "waits = pd.Series([2, 3, 3, 4, 4, 5, 6, 7, 12, 13])\n",
    "\n",
    "print(\"Median wait:\", waits.median())\n",
    "print(\"90th percentile:\", round(np.percentile(waits, 90), 1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### 9. One Large Order\n",
    "# Daily revenue for a week, including one unusually large corporate order.\n",
    "#   1. Compute the mean and median of revenue.\n",
    "#   2. Drop the largest value and compute the mean and median again.\n",
    "#   3. Which statistic changed more?\n",
    "# Print exactly:\n",
    "# Mean with large order: 1100.0\n",
    "# Mean without: 600.0\n",
    "# Median with large order: 600.0\n",
    "# Median without: 600.0\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "revenue = pd.Series([500, 650, 600, 550, 700, 600, 4100])\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input",
     "homework-answer"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean with large order: 1100.0\n",
      "Mean without: 600.0\n",
      "Median with large order: 600.0\n",
      "Median without: 600.0\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "revenue = pd.Series([500, 650, 600, 550, 700, 600, 4100])\n",
    "\n",
    "without = revenue[revenue != revenue.max()]\n",
    "\n",
    "print(\"Mean with large order:\", revenue.mean())\n",
    "print(\"Mean without:\", without.mean())\n",
    "print(\"Median with large order:\", revenue.median())\n",
    "print(\"Median without:\", without.median())\n",
    "# The single large order moves the mean by 500 but does not move the median at all.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### 10. Precision of an Average\n",
    "# Order values have a standard deviation of $12. The standard error of a sample\n",
    "# mean is sd / sqrt(n).\n",
    "#   1. Compute the standard error of the mean order value for n = 36 orders.\n",
    "#   2. Find the sample size that cuts that standard error in half, and compute its SE.\n",
    "# Print exactly:\n",
    "# SE with n=36: 2.0\n",
    "# SE with n=144: 1.0\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "sd = 12\n",
    "\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input",
     "homework-answer"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE with n=36: 2.0\n",
      "SE with n=144: 1.0\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "sd = 12\n",
    "\n",
    "print(\"SE with n=36:\", sd / np.sqrt(36))\n",
    "print(\"SE with n=144:\", sd / np.sqrt(144))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
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    "    <div class='ch08-hw-feedback-row' data-question='q3'><strong>Question 3</strong><span></span></div>\n",
    "    <div class='ch08-hw-feedback-row' data-question='q4'><strong>Question 4</strong><span></span></div>\n",
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    "    <div class='ch08-hw-feedback-row' data-question='q6'><strong>Question 6</strong><span></span></div>\n",
    "    <div class='ch08-hw-feedback-row' data-question='q7'><strong>Question 7</strong><span></span></div>\n",
    "    <div class='ch08-hw-feedback-row' data-question='q8'><strong>Question 8</strong><span></span></div>\n",
    "    <div class='ch08-hw-feedback-row' data-question='q9'><strong>Question 9</strong><span></span></div>\n",
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    "        return payload;\n",
    "      });\n",
    "    });\n",
    "  }\n",
    "\n",
    "  function initHomeworkGrader() {\n",
    "    var grader = document.getElementById('ch08-hw-grader');\n",
    "    if (!grader || grader.dataset.ready === 'true') return;\n",
    "    grader.dataset.ready = 'true';\n",
    "\n",
    "    var identity = getParams();\n",
    "    var actions = grader.querySelector('.ch08-hw-actions');\n",
    "    var result = document.getElementById('ch08-hw-result');\n",
    "    var submit = document.getElementById('ch08-hw-submit');\n",
    "    var reset = document.getElementById('ch08-hw-reset');\n",
    "\n",
    "    loadSessionIdentity(identity, actions, submit, result);\n",
    "\n",
    "    submit.addEventListener('click', function () {\n",
    "      clearFeedback(grader);\n",
    "      submit.disabled = true;\n",
    "      result.textContent = 'Submitting homework.';\n",
    "\n",
    "      saveAttempt({\n",
    "        homework_id: homeworkId,\n",
    "        answers: collectAnswers(),\n",
    "        code: collectCodeCells(),\n",
    "        canvas_course_id: identity.canvas_course_id,\n",
    "        canvas_assignment_id: identity.canvas_assignment_id,\n",
    "        canvas_user_id: identity.canvas_user_id\n",
    "      })\n",
    "        .then(function (payload) {\n",
    "          var best = (payload.best_score === null || typeof payload.best_score === 'undefined') ? payload.score : payload.best_score;\n",
    "          var attempt = (payload.attempt_count === null || typeof payload.attempt_count === 'undefined') ? '' : ' Attempt ' + payload.attempt_count + '.';\n",
    "          applyFeedback(grader, payload.feedback || {});\n",
    "          result.textContent = 'Submission saved.' + attempt + ' Score: ' + payload.score + ' / ' + payload.max_score + '. Best score: ' + best + ' / ' + payload.max_score + '. Canvas sync: ' + payload.canvas_sync_status + '.';\n",
    "        })\n",
    "        .catch(function (error) {\n",
    "          result.textContent = 'Could not save this attempt: ' + error.message;\n",
    "        })\n",
    "        .finally(function () {\n",
    "          submit.disabled = false;\n",
    "        });\n",
    "    });\n",
    "\n",
    "    reset.addEventListener('click', function () {\n",
    "      clearFeedback(grader);\n",
    "      result.textContent = '';\n",
    "    });\n",
    "  }\n",
    "\n",
    "  if (document.readyState === 'loading') {\n",
    "    document.addEventListener('DOMContentLoaded', initHomeworkGrader);\n",
    "  } else {\n",
    "    initHomeworkGrader();\n",
    "  }\n",
    "})();\n",
    "</script>\n"
   ]
  }
 ],
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