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[lab-confidence-intervals]Ricardo Mendes #206

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182 changes: 163 additions & 19 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": 1,
"metadata": {},
"outputs": [],
"source": [
"# Libraries"
"# Libraries\n",
"import pandas as pd\n",
"import numpy as np\n",
"import scipy.stats as st"
]
},
{
Expand All @@ -32,11 +35,40 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 4,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample mean: 173.47\n",
"Sample standard deviation: 7.36\n",
"Sample size: 15\n",
"Confidence interval: (170.91, 176.02)\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"\n",
"heights = [167, 167, 168, 168, 168, 169, 171, 172, 173, 175, 175, 175, 177, 182, 195]\n",
"n = len(heights)\n",
"\n",
"sample_mean = np.mean(heights)\n",
"sample_std = np.std(heights, ddof=1)\n",
"\n",
"#t-value for 80% confidence level with n-1 degrees of freedom\n",
"t_value = st.t.ppf(0.9, n-1)\n",
"\n",
"# confidence interval\n",
"CI = (sample_mean - t_value*(sample_std/np.sqrt(n)), sample_mean + t_value*(sample_std/np.sqrt(n)))\n",
"\n",
"\n",
"print(\"Sample mean: {:.2f}\".format(sample_mean))\n",
"print(\"Sample standard deviation: {:.2f}\".format(sample_std))\n",
"print(\"Sample size: {}\".format(n))\n",
"print(\"Confidence interval: ({:.2f}, {:.2f})\".format(CI[0], CI[1]))\n"
]
},
{
Expand All @@ -51,11 +83,36 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 5,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample proportion: 0.26\n",
"80% Confidence interval: (0.20, 0.31)\n",
"90% Confidence interval: (0.19, 0.33)\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"\n",
"n = 105\n",
"p = 27/105\n",
"se = np.sqrt(p*(1-p)/n)\n",
"s\n",
"z_80 = st.norm.ppf(0.9)\n",
"z_90 = st.norm.ppf(0.95)\n",
"\n",
"# confidence intervals\n",
"CI_80 = (p - z_80*se, p + z_80*se)\n",
"CI_90 = (p - z_90*se, p + z_90*se)\n",
"\n",
"print(\"Sample proportion: {:.2f}\".format(p))\n",
"print(\"80% Confidence interval: ({:.2f}, {:.2f})\".format(CI_80[0], CI_80[1]))\n",
"print(\"90% Confidence interval: ({:.2f}, {:.2f})\".format(CI_90[0], CI_90[1]))\n"
]
},
{
Expand All @@ -76,11 +133,31 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample size required: 425\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"\n",
"# set up the problem\n",
"sigma = 4 # population standard deviation\n",
"E = 0.5 # desired error level\n",
"alpha = 0.01 # significance level\n",
"z_alpha_2 = st.norm.ppf(1 - alpha/2) # z-value for given significance level\n",
"\n",
"# calculate sample size\n",
"n = np.ceil((z_alpha_2 * sigma / E) ** 2)\n",
"\n",
"# print the result\n",
"print(\"Sample size required: {}\".format(int(n)))\n"
]
},
{
Expand All @@ -94,11 +171,34 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sample size required: 3138\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"\n",
"# set up the problem\n",
"n = 105 # sample size\n",
"p_hat = 27/105 # sample proportion of businesses with losses\n",
"alpha = 0.2 # significance level (1 - confidence level)\n",
"z_alpha_2 = st.norm.ppf(1 - alpha/2) # z-value for given significance level\n",
"E = 0.01 # desired error level\n",
"\n",
"# calculate sample size\n",
"q_hat = 1 - p_hat\n",
"n_required = ((z_alpha_2**2) * p_hat * q_hat) / (E**2)\n",
"n_required = np.ceil(n_required)\n",
"\n",
"# print the result\n",
"print(\"Sample size required: {}\".format(int(n_required)))\n"
]
},
{
Expand All @@ -121,17 +221,61 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 11,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The 94% confidence interval for the difference in mean durations is [6.30, 25.70].\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"\n",
"#calculate the sample means and standard deviations\n",
"n_x = 40\n",
"x_bar = 418\n",
"sigma_x = 26\n",
"\n",
"n_y = 50\n",
"y_bar = 402\n",
"sigma_y = 22\n",
"\n",
"#calculate the standard error\n",
"se = np.sqrt(sigma_x**2/n_x + sigma_y**2/n_y)\n",
"\n",
"#critical value for a 94% confidence interval\n",
"alpha = 0.06/2 # two-tailed test\n",
"z_critical = st.norm.ppf(1 - alpha)\n",
"\n",
"#construct the confidence interval\n",
"lower_bound = (x_bar - y_bar) - z_critical * se\n",
"upper_bound = (x_bar - y_bar) + z_critical * se\n",
"\n",
"print(f\"The 94% confidence interval for the difference in mean durations is [{lower_bound:.2f}, {upper_bound:.2f}].\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -145,7 +289,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
"version": "3.10.9"
}
},
"nbformat": 4,
Expand Down