A random sample of $16$ order cook times at a restaurant has an average of $24$ minutes and a standard

deviation of $2$ minutes. The order cook time follows a normal distribution. $1.$ Construct a $99\%$ confidence interval for the mean order cook time.

a$)24\backslash$pm $2\mathrm{.}576\backslash$times $0\mathrm{.}5$

b$)24\backslash$pm $2\mathrm{.}947\backslash$times $0\mathrm{.}5$

c$)24\backslash$pm $2\mathrm{.}921\backslash$times $0\mathrm{.}5$

d$)24\backslash$pm $2\mathrm{.}576\backslash$times $0\mathrm{.}125$

e$)24\backslash$pm $2\mathrm{.}947\backslash$times $0\mathrm{.}125$

$12.$ Is there enough evidence to conclude the average order cook time is different from $23$ minutes.

Carry out an appropriate hypothesis test. What are the test statistic and the P$-$value range? Assume

all necessary assumptions hold.

a$)$ TS $=2\mathrm{.}000$; $0\mathrm{.}025<$ p$-$value $<0\mathrm{.}05.$

b$)$ TS $=2\mathrm{.}000$; $0\mathrm{.}05<$ p$-$value $<0\mathrm{.}10.$

c$)$ TS $=2\mathrm{.}000$; p$-$value $>0\mathrm{.}10.$

d$)$ TS $=-2\mathrm{.}000$; $0\mathrm{.}05<$ p$-$value $<0\mathrm{.}10.$

e$)$ TS $=-2\mathrm{.}000$; $0\mathrm{.}025<$ p$-$value $<0\mathrm{.}05.$