a$)$ Write a function of the form

function ci $=$ hrci$($B$,$ alpha$)$

that takes the number of bootstrap replicates $$ and the confidence level $$ as input argu$-$

ments and returns an $$ confidence interval for HR$.($Run your function with $>=1,000$

to get reliable estimates.$)$ For example, hrci$(1000,0\mathrm{.}95)$ should return a $95\%$ confidence

interval based on $1,000$ bootstrap replicates.

Hint: sort$($hr$)$ returns a sorted list of hazard ratios. For example, if $=1,000$ and

$=0\mathrm{.}95,$ then the required confidence interval can be found with

hr $=$ sort$($hr$)$; $\%$ overwrite with sorted array

ci $=[$hr$(25),$ hr$(975)]$;

Your code should work with any positive value of $$ and any value of $$ between $0$ and $1.$

$($You do not need to check that $0<<1$ in your code.$)$ The expression round$($B$(1$

alpha$)/2)$ returns the nearest integer index in the sorted array corresponding to the

lower $(1)/2$ point of the confidence interval. You will need to determine an analo$-$

gous expression for the upper index. Include a copy of your code in your writeup.

$($b$)$ Run your code five times with $=1000$ and $=0\mathrm{.}95$ and list the results that you

get