In a study comparing banks in two countries, a sample of $144$ matched pairs of banks was formed. Each pair contained one bank from country $x$ and one from country $y.$ The pairings were made in such a way that the two members were as similar as possible in regard to such factors as size and age. The ratio of total loans outstanding to total assets was calculated for each of the banks. For this ratio, the sample mean difference $($country $x-$ country y$)$ was $0\mathrm{.}0492,$ and the sample standard deviation of the differences was $0\mathrm{.}3113.$ Test, against a two$-$sided alternative, the null hypothesis that the two population means are equal. $($Assume $=0\mathrm{.}01.)$

Click the icon to view the critical values of the Student's $t$ distribution.

Which of the following correctly states $H_0$ and $H_1?$

A$.$

$H_0$:${}_x-{}_{y}0$

$H_1$:${}_x-{}_y=0$

C$.$

$H_0$:${}_x-{}_y=0$

$H_1$:${}_x-{}_y<0$

E$.$

$H_0$:${}_x-{}_y=0$

$H_1$:${}_x-{}_{y}0$

B$.$

$H_0$:${}_x-{}_y=0$

$H_1$:${}_x-{}_{y}0$

D$.$

$]=[0$

The test statistic is $t=1\mathrm{.}897.($Round to three decimal places as needed.$)$

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

$($Round to three decimal places as needed. Use a comma to separate answers as needed.$)$taking the preparation course.

Click the icon to view the data table.

Click the icon to view the critical values of the Student's $t$ distribution.

A$.$

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

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

D$.$

$H_0$:${}_1-{}_2>0$

$H_1$:${}_1-{}_{2}0$

B$.$

$H_0$:${}_1-{}_2<0$

$H_1$:${}_1-{}_{2}0$

E$.$

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

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

C$.$

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

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

F$.$

$H_0$:${}_1-{}_2=0$

$H_1$:${}_1-{}_{2}0$

The test statistic is $t=$

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

Achievement test scores

$\backslash$table$[[$Sample$,$Took course,$\backslash$table$[[$Did not take$],[$course$]]],[1,65,47],[2,82,73],[3,60,78],[4,92,88],[5,86,79],[6,87,80],[7,71,56],[8,76,64],[9,85,77],[10,84,76],[11,99,98],[12,73,59],[13,74,61],[14,70,55],[15,91,86],[16,62,85],[17,75,62],[18,72,58],[19,79,68],[20,68,52]]$