Consider the hypothesis statement shown below using $=0\mathrm{.}10$ and the data to the right from two independent sampies.

$H_0$:${}_1-{}_{2}0$

$H_1$:${}_1-{}_2<0$

Consider the hypothesis statement shown below using $=0\mathrm{.}10$ and the data to the right from two independent samples.

${\stackrel{}{x}}_1=124,{\stackrel{}{x}}_2=137$

${}_1=45,{}_2=34$

$n_1=50,n_2=35$

$H_0$:${}_1-{}_{2}0$

$H_1$:${}_1-{}_2<0$

a$)$ Calculate the appropriate test statistic and interpret the result.

b$)$ Calculate the $p-$value and interpret the result.

Click here to view page $1$ of the standard normal table. Click here to view page $2$ of the standard normal table.

a$)$ The test statistic is

$($Round to two decimal places as needed.$)$

Determine the appropriate critical value$($s$).$

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

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

Since the test statistic in the rejection region, $H_0.$ There is evidence to conclude that the mean of population $1$ is less than the mean of population $2.$

b$)$ The $p-$value is

$($Round to three decimal places as needed.$)$

Since the p$-$value is $H_0.$ There is evidence to conclude that the mean of population $1$ is less than the mean of population $2.$

${}_1=45,{}_2=34$

$n_1=50,n_2=35$

a$)$ Calculate the appropriate test statistic and interpret the result.

b$)$ Calculate the p$-$value and interpret the result.

Click here to view page $1$ of the standard normal table. Click here to view page $2$ of the standard normal table.

a$)$ The test statistic is

$($Round to two decimal places as needed.$)$

Determine the appropriate critical value$($s$).$

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

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

Since the test statistic $,$ in the rejection region, $H_0.$ There is evidence to conclude that the mean of population $1$ is less than the mean of population $2.$

b$)$ The p$-$value is

$($Round to three decimal places as needed.$)$

Since the p$-$value is $,|{}_1,|H_0.$ There is $,$ evidence to conclude that the mean of population $1$ is less than the mean of population $2.$