assignment_38.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b5db3773-8373-47fe-8677-cf5958996719",
   "metadata": {},
   "source": [
    "Q1. Calculate the 95% confidence interval for a sample of data with a mean of 50 and a standard deviation\n",
    "of 5 using Python. Interpret the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0254b1e4-950d-4a19-8d7b-add996dc4dc4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% Confidence Interval: (49.02001800772997, 50.97998199227003)\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "# Given data\n",
    "mean = 50\n",
    "std_dev = 5\n",
    "sample_size = 100  # You should replace this with your actual sample size\n",
    "\n",
    "# Calculate the critical value for a 95% confidence interval\n",
    "z_score = stats.norm.ppf(0.975)  # For a two-tailed test\n",
    "\n",
    "# Calculate the margin of error\n",
    "margin_of_error = z_score * (std_dev / (sample_size ** 0.5))\n",
    "\n",
    "# Calculate the confidence interval\n",
    "confidence_interval = (mean - margin_of_error, mean + margin_of_error)\n",
    "\n",
    "# Display the results\n",
    "print(f\"95% Confidence Interval: {confidence_interval}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc398535-1716-4683-bc72-93bf2c5fc14b",
   "metadata": {},
   "source": [
    "Q2. Conduct a chi-square goodness of fit test to determine if the distribution of colors of M&Ms in a bag\n",
    "matches the expected distribution of 20% blue, 20% orange, 20% green, 10% yellow, 10% red, and 20%\n",
    "brown. Use Python to perform the test with a significance level of 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad6db8be-0f62-48a8-bf2b-9cf87c0a0150",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-square statistic: 3.6999999999999997\n",
      "P-value: 0.5933639617818078\n",
      "Fail to reject the null hypothesis. The distribution of colors in M&Ms matches the expected distribution.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chisquare\n",
    "\n",
    "# Given data\n",
    "observed_counts = np.array([18, 22, 15, 8, 12, 25])  # Replace these values with your actual observed counts\n",
    "expected_counts = np.array([20, 20, 20, 10, 10, 20])\n",
    "\n",
    "# Perform the chi-square goodness of fit test\n",
    "chi2_stat, p_value = chisquare(f_obs=observed_counts, f_exp=expected_counts)\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# Print the results\n",
    "print(f\"Chi-square statistic: {chi2_stat}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. The distribution of colors in M&Ms is not as expected.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. The distribution of colors in M&Ms matches the expected distribution.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5eeff7e-3070-4f1f-8f1f-4619b2295b80",
   "metadata": {},
   "source": [
    "Q3. Use Python to calculate the chi-square statistic and p-value for a contingency table with the following\n",
    "data:\n",
    "       Group A Group B\n",
    "\n",
    "Outcome 1 20 15\n",
    "Outcome 2 10 25\n",
    "Outcome 3 15 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f0f93074-f70c-4661-a2d0-26bf6247932b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-square statistic: 5.833333333333334\n",
      "P-value: 0.05411376622282158\n",
      "Fail to reject the null hypothesis. There is no significant association between Group and Outcome.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chi2_contingency\n",
    "\n",
    "# Given data\n",
    "observed_data = np.array([[20, 15], [10, 25], [15, 20]])\n",
    "\n",
    "# Perform the chi-square test for independence\n",
    "chi2_stat, p_value, _, _ = chi2_contingency(observed_data)\n",
    "\n",
    "# Print the results\n",
    "print(f\"Chi-square statistic: {chi2_stat}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. There is a significant association between Group and Outcome.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no significant association between Group and Outcome.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2388c844-507f-4f80-91f7-70fb393155a5",
   "metadata": {},
   "source": [
    "Q4. A study of the prevalence of smoking in a population of 500 individuals found that 60 individuals\n",
    "smoked. Use Python to calculate the 95% confidence interval for the true proportion of individuals in the\n",
    "population who smoke."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c0232df8-ee70-4345-8923-dc5fa4ed01df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% Confidence Interval for smoking prevalence: (0.09151638887130707, 0.1484836111286929)\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "import math\n",
    "\n",
    "# Given data\n",
    "sample_proportion = 60 / 500  # Smoking prevalence in the sample\n",
    "sample_size = 500\n",
    "confidence_level = 0.95\n",
    "\n",
    "# Calculate the critical value for a 95% confidence interval\n",
    "z_score = stats.norm.ppf((1 + confidence_level) / 2)\n",
    "\n",
    "# Calculate the margin of error\n",
    "margin_of_error = z_score * math.sqrt((sample_proportion * (1 - sample_proportion)) / sample_size)\n",
    "\n",
    "# Calculate the confidence interval\n",
    "confidence_interval = (sample_proportion - margin_of_error, sample_proportion + margin_of_error)\n",
    "\n",
    "# Display the results\n",
    "print(f\"95% Confidence Interval for smoking prevalence: {confidence_interval}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362d4467-2db6-46be-9b0b-9bf9f0430c4d",
   "metadata": {},
   "source": [
    "Q5. Calculate the 90% confidence interval for a sample of data with a mean of 75 and a standard deviation\n",
    "of 12 using Python. Interpret the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b67c0749-7d6e-4cd6-bc3d-977a743e4007",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90% Confidence Interval: (71.27739919800369, 78.72260080199631)\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "# Given data\n",
    "mean = 75\n",
    "std_dev = 12\n",
    "sample_size = 30  # You should replace this with your actual sample size\n",
    "confidence_level = 0.90\n",
    "\n",
    "# Calculate the critical value for a 90% confidence interval\n",
    "t_score = stats.t.ppf((1 + confidence_level) / 2, df=sample_size - 1)\n",
    "\n",
    "# Calculate the margin of error\n",
    "margin_of_error = t_score * (std_dev / (sample_size ** 0.5))\n",
    "\n",
    "# Calculate the confidence interval\n",
    "confidence_interval = (mean - margin_of_error, mean + margin_of_error)\n",
    "\n",
    "# Display the results\n",
    "print(f\"90% Confidence Interval: {confidence_interval}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3e3ca46-be9f-4156-9cb1-48f93579379c",
   "metadata": {},
   "source": [
    "Q6. Use Python to plot the chi-square distribution with 10 degrees of freedom. Label the axes and shade the\n",
    "area corresponding to a chi-square statistic of 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "67db208a-3c9d-472b-81c1-eab143de74bf",
   "metadata": {},
   "outputs": [
    {
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\n",
      "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",
    "import scipy.stats as stats\n",
    "\n",
    "# Parameters\n",
    "degrees_of_freedom = 10\n",
    "chi2_statistic = 15\n",
    "\n",
    "# Generate x values\n",
    "x = np.linspace(0, 30, 1000)\n",
    "\n",
    "# Plot the chi-square distribution\n",
    "plt.plot(x, stats.chi2.pdf(x, degrees_of_freedom), label=f'Chi-Square Distribution (df={degrees_of_freedom})')\n",
    "\n",
    "# Shade the area corresponding to a chi-square statistic of 15\n",
    "plt.fill_between(x, 0, stats.chi2.pdf(x, degrees_of_freedom), where=(x >= chi2_statistic), color='gray', alpha=0.5)\n",
    "\n",
    "# Add labels and title\n",
    "plt.xlabel('Chi-Square Statistic')\n",
    "plt.ylabel('Probability Density Function (PDF)')\n",
    "plt.title(f'Chi-Square Distribution with {degrees_of_freedom} Degrees of Freedom')\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea9d8a5c-3c54-4a60-a183-b794c0e6b9c7",
   "metadata": {},
   "source": [
    "Q7. A random sample of 1000 people was asked if they preferred Coke or Pepsi. Of the sample, 520\n",
    "preferred Coke. Calculate a 99% confidence interval for the true proportion of people in the population who\n",
    "prefer Coke."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aea092de-f739-460a-b8d0-10f16360e9eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "99% Confidence Interval for preference of Coke: (0.4793051576779699, 0.5606948423220302)\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "import math\n",
    "\n",
    "# Given data\n",
    "sample_proportion = 520 / 1000  # Preferred Coke in the sample\n",
    "sample_size = 1000\n",
    "confidence_level = 0.99\n",
    "\n",
    "# Calculate the critical value for a 99% confidence interval\n",
    "z_score = stats.norm.ppf((1 + confidence_level) / 2)\n",
    "\n",
    "# Calculate the margin of error\n",
    "margin_of_error = z_score * math.sqrt((sample_proportion * (1 - sample_proportion)) / sample_size)\n",
    "\n",
    "# Calculate the confidence interval\n",
    "confidence_interval = (sample_proportion - margin_of_error, sample_proportion + margin_of_error)\n",
    "\n",
    "# Display the results\n",
    "print(f\"99% Confidence Interval for preference of Coke: {confidence_interval}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c579704f-1501-433b-911b-d569b2dd877e",
   "metadata": {},
   "source": [
    "Q8. A researcher hypothesizes that a coin is biased towards tails. They flip the coin 100 times and observe\n",
    "45 tails. Conduct a chi-square goodness of fit test to determine if the observed frequencies match the\n",
    "expected frequencies of a fair coin. Use a significance level of 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8533fa80-d665-4b82-ba7d-edbb2fd26e63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-square statistic: 1.0\n",
      "P-value: 0.31731050786291115\n",
      "Fail to reject the null hypothesis. There is no evidence of bias towards tails.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chisquare\n",
    "\n",
    "# Given data\n",
    "observed_frequencies = np.array([45, 55])  # Observed tails, observed heads\n",
    "expected_frequencies = np.array([50, 50])  # Expected frequencies for a fair coin\n",
    "\n",
    "# Perform the chi-square goodness of fit test\n",
    "chi2_stat, p_value = chisquare(f_obs=observed_frequencies, f_exp=expected_frequencies)\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# Print the results\n",
    "print(f\"Chi-square statistic: {chi2_stat}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. The coin may be biased towards tails.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no evidence of bias towards tails.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd6432ad-6684-4a8a-8827-7f0a805c0e5b",
   "metadata": {},
   "source": [
    "Q9. A study was conducted to determine if there is an association between smoking status (smoker or\n",
    "non-smoker) and lung cancer diagnosis (yes or no). The results are shown in the contingency table below.\n",
    "Conduct a chi-square test for independence to determine if there is a significant association between\n",
    "smoking status and lung cancer diagnosis.\n",
    "\n",
    "       Lung Cancer: Yes           Lung Cancer: No\n",
    "\n",
    "Smoker           60                140\n",
    "Non-smoker        30               170"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f339b114-146c-4b91-8c8f-53abb15fb76b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-square statistic: 12.057347670250895\n",
      "P-value: 0.0005158863863703744\n",
      "Reject the null hypothesis. There is a significant association between smoking status and lung cancer diagnosis.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chi2_contingency\n",
    "\n",
    "# Given data\n",
    "observed_data = np.array([[60, 140], [30, 170]])\n",
    "\n",
    "# Perform the chi-square test for independence\n",
    "chi2_stat, p_value, _, _ = chi2_contingency(observed_data)\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# Print the results\n",
    "print(f\"Chi-square statistic: {chi2_stat}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. There is a significant association between smoking status and lung cancer diagnosis.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no significant association between smoking status and lung cancer diagnosis.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d9f2a78-ccf7-4329-aa1f-5295a5e27e25",
   "metadata": {},
   "source": [
    "Q10. A study was conducted to determine if the proportion of people who prefer milk chocolate, dark\n",
    "chocolate, or white chocolate is different in the U.S. versus the U.K. A random sample of 500 people from\n",
    "the U.S. and a random sample of 500 people from the U.K. were surveyed. The results are shown in the\n",
    "contingency table below. Conduct a chi-square test for independence to determine if there is a significant\n",
    "association between chocolate preference and country of origin.\n",
    "\n",
    "           Milk Chocolate   Dark Chocolate   White Chocolate\n",
    "\n",
    "U.S. (n=500)   200           150               150\n",
    "U.K. (n=500)   225           175               100\n",
    "\n",
    "Use a significance level of 0.01."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "873832a4-6978-4296-abc8-ff31781bab13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-square statistic: 13.393665158371041\n",
      "P-value: 0.0012348168997745918\n",
      "Reject the null hypothesis. There is a significant association between chocolate preference and country of origin.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import chi2_contingency\n",
    "\n",
    "# Given data\n",
    "observed_data = np.array([[200, 150, 150], [225, 175, 100]])\n",
    "\n",
    "# Perform the chi-square test for independence\n",
    "chi2_stat, p_value, _, _ = chi2_contingency(observed_data)\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.01\n",
    "\n",
    "# Print the results\n",
    "print(f\"Chi-square statistic: {chi2_stat}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. There is a significant association between chocolate preference and country of origin.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is no significant association between chocolate preference and country of origin.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1e5c76-f2a5-4be1-a992-ba456a1368c0",
   "metadata": {},
   "source": [
    "Q11. A random sample of 30 people was selected from a population with an unknown mean and standard\n",
    "deviation. The sample mean was found to be 72 and the sample standard deviation was found to be 10.\n",
    "Conduct a hypothesis test to determine if the population mean is significantly different from 70. Use a\n",
    "significance level of 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "58b486d0-52e4-4bbe-913e-ca5282476548",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T-statistic: inf\n",
      "P-value: 0.0\n",
      "Reject the null hypothesis. The population mean is significantly different from 70.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_77/3154871197.py:10: RuntimeWarning: Precision loss occurred in moment calculation due to catastrophic cancellation. This occurs when the data are nearly identical. Results may be unreliable.\n",
      "  t_statistic, p_value = stats.ttest_1samp([sample_mean]*sample_size, population_mean)\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "# Given data\n",
    "sample_mean = 72\n",
    "sample_std_dev = 10\n",
    "sample_size = 30\n",
    "population_mean = 70\n",
    "\n",
    "# Perform a one-sample t-test\n",
    "t_statistic, p_value = stats.ttest_1samp([sample_mean]*sample_size, population_mean)\n",
    "\n",
    "# Set the significance level\n",
    "alpha = 0.05\n",
    "\n",
    "# Print the results\n",
    "print(f\"T-statistic: {t_statistic}\")\n",
    "print(f\"P-value: {p_value}\")\n",
    "\n",
    "# Make a decision\n",
    "if p_value < alpha:\n",
    "    print(\"Reject the null hypothesis. The population mean is significantly different from 70.\")\n",
    "else:\n",
    "    print(\"Fail to reject the null hypothesis. There is not enough evidence to suggest a significant difference in the population mean.\")\n"
   ]
  }
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