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152 changes: 144 additions & 8 deletions your-code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -9,11 +9,13 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Libraries"
"import pandas as pd\n",
"import numpy as np\n",
"import scipy.stats as st\n"
]
},
{
Expand All @@ -30,13 +32,96 @@
"**Hint**: function `stats.norm.interval` from `scipy` can help you get through this exercise. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"173.46666666666667"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]\n",
"\n",
"heights_sum = sum(heights)\n",
"\n",
"heights_sum/15"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(172.14308590115726, 174.79024743217607)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]\n",
"\n",
"alpha = 0.8\n",
"\n",
"mean = heights_sum/15\n",
"\n",
"std = 4\n",
"\n",
"n = 15\n",
"\n",
"st.norm.interval(0.8, loc=mean, scale = std/np.sqrt(n))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(170.9117270472475, 176.02160628608584)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## same using t-distribution\n",
"\n",
"heights = np.array([167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195])\n",
"\n",
"s = heights.std(ddof=1)\n",
"mean = heights.mean()\n",
"n = len(heights)\n",
"\n",
"st.t.interval(0.8, n-1, loc = mean, scale = s/np.sqrt(n))\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
"## t-interval are fatter on the tail, allow more extreme values"
]
},
{
Expand All @@ -51,11 +136,62 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 27,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Our CI with 80% level of confidence for proportion is [0.20248138545542083, 0.3118043288302934]\n"
]
}
],
"source": [
"# your code here"
"sample_size = 105\n",
"losses = 27\n",
"\n",
"p = losses/sample_size\n",
"\n",
"n = 105\n",
"\n",
"# 80% confidence\n",
"\n",
"z_value = st.norm.ppf( 1 - (1 - 0.8)/2)\n",
"\n",
"margin_of_error = z_value * np.sqrt((p * (1- p))/n)\n",
"\n",
"lower_bound = p - margin_of_error\n",
"upper_bound = p + margin_of_error\n",
"\n",
"print(f\"Our CI with 80% level of confidence for proportion is [{lower_bound}, {upper_bound}]\")\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Our CI with 80% level of confidence for proportion is [0.18698561776452813, 0.3273000965211861]\n"
]
}
],
"source": [
"# 90% confidence\n",
"\n",
"z_value = st.norm.ppf( 1 - (1 - 0.9)/2)\n",
"\n",
"margin_of_error = z_value * np.sqrt((p * (1- p))/n)\n",
"\n",
"lower_bound = p - margin_of_error\n",
"upper_bound = p + margin_of_error\n",
"\n",
"print(f\"Our CI with 80% level of confidence for proportion is [{lower_bound}, {upper_bound}]\")"
]
},
{
Expand Down Expand Up @@ -131,7 +267,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -145,7 +281,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
"version": "3.10.9"
}
},
"nbformat": 4,
Expand Down