The accompanying table shows two samples that were collected as matched pairs. Complete parts $($a$)$ through $($d$)$ below.

Click the icon to view the data table.

a$.$ State the null and alternative hypotheses to test if the population represented by Sample $1$ has a higher mean than the population represented by Sample $2.$ Let ${}_d$ be the population mean of matched$-$pair differences for Sample $1$ minus Sample $2.$ Choose the correct answer below.

A$.$

$H_0$:${}_{d}0$

$H_1$:${}_d<0$

c$.$

$H_0$:${}_d<0$

$H_1$:${}_{d}0$

E$.$

$H_0$:${}_d=0$

$H_1$:${}_{d}0$

B$.$

$H_0$:${}_{d}0$

$H_1$:${}_d=0$

D$.$

$H_0$:${}_{d}0$

$H_1$:${}_d>0$

F$.$

$H_0$:${}_{d}0$

$H_1$:${}_{d}0$

b$.$ Calculate the appropriate test statistic and interpret the results of the hypothesis test using $=0\mathrm{.}05.$

The test statistic is $($Round to two decimal places as needed.$)$

The critical value$($s$)$ is$($are$)$

$($Use a comma to separate answers as needed. Round to two decimal places as needed.$)$

Interpret the results of the hypothesis test.

Since the test statistic the critical value$($s$),$ the null hypothesis. There is evidence that the mean of Sample $1$ is higher than the mean of Sample $2.$

c$.$ Identify the $p-$value and interpret the result.

p$-$value $=,($Round to three decimal places as needed.

ss program claims that participants will lose an average of more than $10$ pound ight individuals before and after the program. Complete parts $($a$)$ through $($e$)$ be con to view the data table.

n $80\%$ confidence interval to estimate the average weight loss for individuals in the