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just follow the instuction from top to bottom write some function and plot the diagram
involve Python, linear algebra, confidence level, bootstrap linear_model{
“cells”: [
{
“cell_type”: “markdown”,
“source”: [
“n”,
“# Assignment 04: Confidence Intervals & The Bootstrapn”,
“n”,
“Once you are finished, ensure to complete the following steps.n”,
“1. Restart your kernel by clicking ‘Kernel’ > ‘Restart & Run All’.n”,
“2. Fix any errors which result from this.n”,
“3. Repeat steps 1. and 2. until your notebook runs without errors.n”,
]
},
{
“cell_type”: “code”,
“execution_count”: null,
“outputs”: [],
“source”: [
“# Add the necessary imports for this homework n”,
“import numpy as npn”,
“import pandas as pdn”,
“import matplotlib.pyplot as pltn”,
“import seaborn as snsn”,
“import sklearn.model_selectionn”,
“import sklearn.linear_model”
]
},
{
“cell_type”: “markdown”,
“source”: [
“### Question 1: /10pts n”,
“In this question, you will construct a confidence interval for the sample mean, not using the normal distribution, but the t-distribution (see end of lecture 4.3), which is more accurate for small sample sizes. n”,
“n”,
“The $100(1-\alpha)\%$ confidence interval is n”,
“n”,
“$$\bar{x} \pm t_{1-\alpha/2, n-1} \dfrac{\hat{\sigma}}{\sqrt{n}}$$n”,
“n”,
“Where $t_{1-\alpha/2, n-1}$ is the appropiorate quantile of a Student’s t distribution with $n-1$ degrees of freedom. n”,
“Write a function called confidence_interval which takes as it’s argument an array of data called data and returns two things:n”,
“n”,
“* An estimated mean of data, and n”,
“n”,
“* The lower and upper bounds of the 95% confidence interval for the mean of data. Ensure these are returned in a numpy array of shape (2,)n”,
“n”,
“To get the appropirate quantiles for the t-distribution, you can use scipy.stats.t, which implements some statistical functions for the t-distribution. Take a look at the documentation for scipy.stats.t, especially the ppf method.n”,
“n”,
“Here is the documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.htmln”
]
},
{
“cell_type”: “code”,
“execution_count”: null,
“outputs”: [],
“source”: [
“def confidence_interval(data):n”,
“n”,
” # Note, np.std divides by n and not n-1n”,
” # Force it to apply the correct formula by ussing ddof=1n”,
” # Alternaively, you can use scipy.stats.sem to computen”,
” #The standard errorn”,
” n”,
” return estimated_mean, bounds”
]
},
{
“cell_type”: “markdown”,