Please do the following in RStudio code

See photo for info

Question $1\mathrm{.}1[3$ pts$]$

Write a function from scratch that accepts the number of successes and sample size then calculates and prints

the $99\%$ z$-$confidence interval the population proportion. Test your function using a sample where there are

$800$ successes out of $2000$ observations.

You can recycle code from module $3($the reference files may be useful$).$

Question $1\mathrm{.}2[2$ pts$]$

Using the same data as in question $1\mathrm{.}2,$ write one line of code that calculates the $99\%-$confidence interval.

Use the function prop.test and the argument correct$-$FALSE.

Question $1\mathrm{.}3[2$ pts$]$

Compare the runtime of your user$-$defined function versus the built in function. Which is faster? Hint:

proc.time or microbenchmark may be useful.