A fabric manufacturer believes that the proportion p of orders arriving late from a certain supplier of raw material exceeds $20\%.$ To test this claim, the manufacturer collects a

sample of $15$ orders and records $x=$ the number of orders in the sample that had been late. You can assume the orders are independent of each other, in terms of tardiness. The

manufacturer wants to bring this problem up and confront the supplier only if they are certain in the claim with significance level of at most $10\%$

Part $($d$)$

What is the critical value $k$ that gives us the test with significance level not exceeding $0\mathrm{.}10?$ What is the actual significance level $$ of such test?

Write your answer as a vector variable ans of length $2,$ whose first component is $k$ and the second is the significance level $.$ For example, if you thin

$k=1$ and $=0\mathrm{.}012345,$ you should write

ans $=c(1,0\mathrm{.}012345)$

Make sure your $R$ code for part $D$ passes all test provided by:

## check whether vector gns is defined

## check whether output is numeric $($or double$)$

if $($test$\_$that$($desc$="",$ code

expect$\_$equal$($is$.$numeric$($gn$$s$),$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$the output is not numeric$/$double$.")$

## check whether output is numeric $($or double$)$

if $($test$\_$that$($desc$=$"the output is not numeric$/$double$.",$ code

expect$\_$equal$($length$($ans$)==2,$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$the output is not numeric$/$double$.")$

And

## check whether the $3$ rd$,4$ th and $5$ th digit of ans are $1,0,5,$ respectively

if $($test$\_$that$($desc$="",$ code

expect$\_$equal$($ floor gns $[2])\%\%1000==105,$ TRUE$)$

$\})!=$ TRUE$)$ stop$("$Sorry$,$ wrong answer"$)$