Q$3[20$pt$]$: A capacitor manufacturer claims that the product's voltage is

at least $100V.$ The voltage of twelve randomly selected capacitors has

been measured to verify this. Below is the R code Bob used to calculate

the $p-$value of the test, along with the output of the results. The values of

the $12$ samples are stored in a vector variable $x$ before running the

following code.

$($a$)[10$pt$]$ Do you agree with Bob's analysis? If yes, would you accept

the company's claim at a significance level of $0\mathrm{.}05?$ If not, how should

the $R$ code be modified and what is your conclusion?

$($b$)[5$pt$]$ Based on the provided information and other R code you may

need, what is the sample standard deviation value for these data?

$($c$)[5$pt$]$ Based on the provided information and other R code you may

need, what is the $90\%$ confidence interval $("$two$-$sided", i$.$e$.,$ the interval

estimate we introduced in lectures$)$ for estimating the mean voltage?

$[$Hint: Note that you do not need the original sample values $x$ to answer

these questions. You may also want to check the documentation of the

t$.$test$()$ function in R$.]$