Esteban, a programming tutor wishes to study the effect that his tutoring has on his students. Esteban

randomly selects $7$ new students and records their current grades in their programming courses. After half

a semester of tutoring, the students' grades are recorded again:

Esteban asks for your help to conduct a paired, two$-$sample hypothesis test at $=0\mathrm{.}10$ to determine if the

tutoring is helping to improve the students' grades. The differences should be computed as BEFORE $-$

AFTER. Where necessary, round results to $4$ decimal places.

a$.$ Which of the following null and alternative hypotheses is appropriate for the test?

$H_0$:${}_d>0$

$H_A$:${}_{d}0$

$H_0$:${}_d=0$

$H_A$:${}_d<mn\; id="EditorElement\_52968">0</mn>$

$H_0$:${}_d=0$

$H_A$:${}_d>0$

$H_0$:${}_d=0$

$H_A$:${}_{d}0$

b$.$ What is the sample mean difference?

${\stackrel{}{x}}_d=$

c$.$ What is the test statistic?

d$.$ What is the p$-$value for the test?

$p-$value $=$

e$.$ What decision results from the test? Select an answer