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solved lab #376

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145 changes: 129 additions & 16 deletions lab-hypothesis-testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,7 +38,7 @@
},
{
"cell_type": "code",
"execution_count": 1,
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"metadata": {},
"outputs": [],
"source": [
Expand All @@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 15,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -278,7 +278,7 @@
"[800 rows x 11 columns]"
]
},
"execution_count": 3,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
Expand All @@ -297,11 +297,40 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 16,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean(Dragon HP): 83.31 | Mean(Other HP): 68.67\n",
"Welch t-statistic: 3.400\n",
"One-sided p-value (Dragon > Others): 0.0008676\n",
"Conclusion: Reject H0: Dragons have higher average HP.\n"
]
}
],
"source": [
"#code here"
"dragons = df[df[\"Type 1\"] == \"Dragon\"][\"HP\"].dropna()\n",
"others = df[df[\"Type 1\"] != \"Dragon\"][\"HP\"].dropna()\n",
"\n",
"t_stat, p_two_sided = st.ttest_ind(dragons, others, equal_var=False, nan_policy=\"omit\")\n",
"\n",
"# Convert two-sided p to one-sided for 'greater' alternative:\n",
"# If mean(dragon) > mean(others), p_one_sided = p_two_sided / 2; else 1 - p_two_sided / 2\n",
"mean_diff = dragons.mean() - others.mean()\n",
"if mean_diff > 0:\n",
" p_one_sided = p_two_sided / 2\n",
"else:\n",
" p_one_sided = 1 - (p_two_sided / 2)\n",
"\n",
"alpha = 0.05\n",
"print(f\"Mean(Dragon HP): {dragons.mean():.2f} | Mean(Other HP): {others.mean():.2f}\")\n",
"print(f\"Welch t-statistic: {t_stat:.3f}\")\n",
"print(f\"One-sided p-value (Dragon > Others): {p_one_sided:.4g}\")\n",
"print(\"Conclusion:\", \"Reject H0: Dragons have higher average HP.\"\n",
" if p_one_sided < alpha else \"Fail to reject H0: Insufficient evidence that Dragons have higher HP.\")\n"
]
},
{
Expand All @@ -313,11 +342,47 @@
},
{
"cell_type": "code",
"execution_count": 18,
"execution_count": 17,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" stat mean_legendary mean_nonlegendary t_stat p_value significant_0.05\n",
" HP 92.738462 67.182313 8.981370 1.002691e-13 True\n",
" Attack 116.676923 75.669388 10.438134 2.520372e-16 True\n",
"Defense 99.661538 71.559184 7.637078 4.826998e-11 True\n",
"Sp. Atk 122.184615 68.454422 13.417450 1.551461e-21 True\n",
"Sp. Def 105.938462 68.892517 10.015697 2.294933e-15 True\n",
" Speed 100.184615 65.455782 11.475044 1.049016e-18 True\n"
]
}
],
"source": [
"#code here"
"stats_cols = [\"HP\", \"Attack\", \"Defense\", \"Sp. Atk\", \"Sp. Def\", \"Speed\"]\n",
"\n",
"leg = df[df[\"Legendary\"] == True]\n",
"non = df[df[\"Legendary\"] == False]\n",
"\n",
"results = []\n",
"for col in stats_cols:\n",
" x = leg[col].dropna()\n",
" y = non[col].dropna()\n",
" t, p = st.ttest_ind(x, y, equal_var=False, nan_policy=\"omit\")\n",
" results.append({\n",
" \"stat\": col,\n",
" \"mean_legendary\": float(np.mean(x)),\n",
" \"mean_nonlegendary\": float(np.mean(y)),\n",
" \"t_stat\": float(t),\n",
" \"p_value\": float(p)\n",
" })\n",
"\n",
"# Present as a small table and mark significance at alpha=0.05 (uncorrected)\n",
"import pandas as pd\n",
"res_df = pd.DataFrame(results)\n",
"res_df[\"significant_0.05\"] = res_df[\"p_value\"] < 0.05\n",
"print(res_df.to_string(index=False))"
]
},
{
Expand All @@ -337,7 +402,7 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 18,
"metadata": {},
"outputs": [
{
Expand Down Expand Up @@ -453,7 +518,7 @@
"4 624.0 262.0 1.9250 65500.0 "
]
},
"execution_count": 5,
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
Expand Down Expand Up @@ -483,10 +548,58 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Close mean: 246951.98213501245\n",
"Far mean: 180678.44105790975\n",
"t-statistic: 3.400096139118546\n",
"p-value: 3.0064957768592614e-301\n",
"Reject H0 → Houses close to school/hospital have significantly different prices.\n"
]
}
],
"source": [
"# Coordinates\n",
"school = (-118, 34)\n",
"hospital = (-122, 37)\n",
"\n",
"# Function to calculate Euclidean distance\n",
"def euclidean_distance(x1, y1, x2, y2):\n",
" return np.sqrt((x1 - x2)**2 + (y1 - y2)**2)\n",
"\n",
"# Calculate distance to school and hospital\n",
"df[\"dist_school\"] = np.sqrt((df[\"longitude\"] - school[0])**2 + (df[\"latitude\"] - school[1])**2)\n",
"df[\"dist_hospital\"] = np.sqrt((df[\"longitude\"] - hospital[0])**2 + (df[\"latitude\"] - hospital[1])**2)\n",
"\n",
"# Close if distance < 0.5 to either\n",
"df[\"close\"] = ((df[\"dist_school\"] < 0.5) | (df[\"dist_hospital\"] < 0.5))\n",
"\n",
"# Split groups\n",
"close_values = df[df[\"close\"] == True][\"median_house_value\"]\n",
"far_values = df[df[\"close\"] == False][\"median_house_value\"]\n",
"\n",
"print(\"Close mean:\", close_values.mean())\n",
"print(\"Far mean:\", far_values.mean())\n",
"\n",
"# --- Hypothesis test ---\n",
"# Two-sample independent t-test\n",
"t_st, p_value = st.ttest_ind(close_values, far_values, equal_var=False)\n",
"\n",
"print(\"t-statistic:\", t_stat)\n",
"print(\"p-value:\", p_value)\n",
"\n",
"# Decision\n",
"alpha = 0.05\n",
"if p_value < alpha:\n",
" print(\"Reject H0 → Houses close to school/hospital have significantly different prices.\")\n",
"else:\n",
" print(\"Fail to reject H0 → No significant difference in prices.\")"
]
},
{
"cell_type": "code",
Expand All @@ -498,7 +611,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -512,7 +625,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.12.7"
}
},
"nbformat": 4,
Expand Down