chapter_4/chi_squared_test.ipynb

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    "import numpy as np\n",
    "import random\n",
    "\n",
    "# Generate 100 random numbers (example)\n",
    "random_numbers = []\n",
    "i = 0\n",
    "while i < 100:\n",
    "    k = random.randint( 0 , 99)\n",
    "    random_numbers.append(k)\n",
    "    i += 1\n",
    "\n",
    "print(\"Random num = \", random_numbers)\n",
    "\n",
    "# Define the expected probabilities for each category (uniform distribution)\n",
    "expected_probs = np.full(10, 10)\n",
    "print(\"expected num in each category = \",expected_probs)\n",
    "\n",
    "\n",
    "# Divide the random numbers into 10 categories\n",
    "observed_counts, _ = np.histogram(random_numbers, bins=10)\n",
    "print(\"frequency = \" , observed_counts)\n",
    "\n",
    "# Calculate the chi-squared statistic\n",
    "chi2_stat = np.sum(abs(observed_counts - expected_probs) ** 2 / (expected_probs))\n",
    "\n",
    "# Calculate the degrees of freedom (number of categories - 1)\n",
    "from scipy.stats import chi2\n",
    "df = 10 - 1  \n",
    "# Calculate the critical value for alpha = 0.05\n",
    "alpha = 0.05\n",
    "critical_value = chi2.ppf(1 - alpha, df)\n",
    "\n",
    "# Print the test results\n",
    "print(\"Chi-squared statistic:\", chi2_stat)\n",
    "print(\"Critical value for alpha 0.05:\", critical_value)\n"
   ]
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