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use this $($ Now imagine that it is year $2034$ and you are working as a public health researcher in the UAE. You are working on a project to assess vaccination coverage for a new global pandemic. The UAE government has implemented a widespread vaccination campaign to combat the spread of the virus and achieve herd immunity. You want to determine the proportion of individuals who have received the new vaccine among a sample of $100$ residents in different parts of the country.

To Begin.

Run the code below. It will provide you with a random sample of $100$ residents. It will save this data to a CSV file called "Vaccinated.csv$".$ Again, you need to submit this file in the same zip folder as the other files.$)$ this is the code: # Load the following libraries so that they can be applied in the subsequent code blocks

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

import random

import scipy.stats as stats

# Run this code. It will generate data and save it to a CSV file called "Vaccinated.csv$".$ You need to submit it in the same zip folder as your other files.

try:

Vaccinated $=$ pd$.$read$\_$csv$(\text{'}$Vaccinated$.$csv$\text{'})$

except FileNotFoundError:

num$\_$samples $=100$

vaccinated $=$ np$.$random.choice$(["$Yes$","$No$"],$ size$=$num$\_$samples$)$

Vaccinated $=$ pd$.$DataFrame$(\{\text{'}$Vaccinated$\text{'}$: vaccinated$\})$

Vaccinated.to$\_$csv$(\text{'}$Vaccinated$.$csv$\text{'})$

# Have a look at Vaccinated dataset.

Vaccinated.head$()$ and this is the output

Vaccinated

$0$ No

$1$ No

$2$ No

$3$ No

$4$ No

and answer this Question $4$a$.$ What is the proportion of people who have received the vaccine $($based on the dataset you have$)?$ keep it in pargaraph format and keep it conciseQuestion $4$b$.$ Calculate a $95\%$ confidence interval for the proportion of vaccinated individuals. What does this

interval tell us about the likely range of vaccination coverage in the entire population? Show your work.

Question $4c.$ What sample size would be required to estimate the proportion of vaccinated individuals in the

country with a $95\%$ confidence level and a margin of error of $0\mathrm{.}02?$ Show your work.