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[lab-confidence-intervals] Carlos Silva #208

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133 changes: 116 additions & 17 deletions your-code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -9,11 +9,14 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# Libraries"
"import pandas as pd\n",
"import numpy as np\n",
"import scipy.stats as st\n",
"import math "
]
},
{
Expand All @@ -32,11 +35,34 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
"heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence Interval: (171.0323076132764, 175.90102572005694)\n"
]
}
],
"source": [
"sample_mean = np.mean(heights)\n",
"sample_std = np.std(heights, ddof=1) \n",
"confidence_level = 0.80\n",
"sample_size = len(heights)\n",
"margin_of_error = st.norm.ppf((1 + confidence_level) / 2) * (sample_std / np.sqrt(sample_size))\n",
"confidence_interval = (sample_mean - margin_of_error, sample_mean + margin_of_error)\n",
"print(\"Confidence Interval:\", confidence_interval)"
]
},
{
Expand All @@ -51,11 +77,29 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence Interval (level 0.8): (0.20248138545542083, 0.3118043288302934)\n",
"Confidence Interval (level 0.9): (0.18698561776452813, 0.3273000965211861)\n"
]
}
],
"source": [
"# your code here"
"total_shops = 105\n",
"shops_with_losses = 27\n",
"sample_proportion = shops_with_losses / total_shops\n",
"confidence_levels = [0.80, 0.90]\n",
"\n",
"for confidence_level in confidence_levels:\n",
" \n",
" margin_of_error = st.norm.ppf((1 + confidence_level) / 2) * np.sqrt((sample_proportion * (1 - sample_proportion)) / total_shops)\n",
" confidence_interval = (sample_proportion - margin_of_error, sample_proportion + margin_of_error)\n",
" print(f\"Confidence Interval (level {confidence_level}):\", confidence_interval)"
]
},
{
Expand All @@ -76,11 +120,32 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# your code here"
"heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Required Sample Size: 425\n"
]
}
],
"source": [
"z_alpha_2 = 2.576 \n",
"sigma = 4 \n",
"error_level = 0.5 \n",
"required_sample_size = math.ceil((z_alpha_2 * sigma / error_level)**2)\n",
"print(\"Required Sample Size:\", required_sample_size)"
]
},
{
Expand All @@ -94,11 +159,26 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Required Sample Size: 3140\n"
]
}
],
"source": [
"# your code here"
"z_alpha_2 = 1.282 \n",
"error_level = 0.01 \n",
"n_total = 105\n",
"n_losses = 27\n",
"p = n_losses / n_total\n",
"q = 1 - p\n",
"required_sample_size = math.ceil((z_alpha_2 ** 2 * p * q) / (error_level ** 2))\n",
"print(\"Required Sample Size:\", required_sample_size)"
]
},
{
Expand All @@ -121,17 +201,36 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Confidence Interval: (6.303419026585921, 25.69658097341408)\n"
]
}
],
"source": [
"# your code here"
"mean_X = 418\n",
"mean_Y = 402\n",
"stddev_X = 26\n",
"stddev_Y = 22\n",
"sample_size_X = 40\n",
"sample_size_Y = 50\n",
"confidence_level = 0.94\n",
"SE = math.sqrt((stddev_X**2 / sample_size_X) + (stddev_Y**2 / sample_size_Y))\n",
"z_score = abs(st.norm.ppf((1 + confidence_level) / 2))\n",
"margin_of_error = z_score * SE\n",
"confidence_interval = (mean_X - mean_Y - margin_of_error, mean_X - mean_Y + margin_of_error)\n",
"print(\"Confidence Interval:\", confidence_interval)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -145,7 +244,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
"version": "3.10.9"
}
},
"nbformat": 4,
Expand Down