You wish to test the following claim $(H_a)$ at a significance level of $=0\mathrm{.}05.$ For the context of this

problem, ${}_d={}_2-{}_1$ where the first data set represents a pre$-$test and the second data set represents a

post$-$test.

$H_o$:${}_d=0$

$H_a$:${}_{d}0$

You believe the population of difference scores is normally distributed, but you do not know the standard

deviation. You obtain pre$-$test and post$-$test samples for $n=4$ subjects. The average difference $($post $-$

pre$)$ is $\frac{?}{\text{b}\text{a}\text{r}}(d)=-20\mathrm{.}9$ with a standard deviation of the differences of $s_d=34\mathrm{.}9.$

What is the critical value for this test? $($Report answer accurate to three decimal places.$)$

critical value $=+-$

What is the test statistic for this sample? $($Report answer accurate to three decimal places.$)$

test statistic $=$

The $p-$value is$...$

smaller than or equal to significance level

greater than significance level

This $p-$value leads to a decision to$...$

reject the null

accept the null

fail to reject the nullAs such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the mean difference of post$-$test

from pre$-$test is not equal to $0.$

There is not sufficient evidence to warrant rejection of the claim that the mean difference of post$-$

test from pre$-$test is not equal to $0.$

The sample data support the claim that the mean difference of post$-$test from pre$-$test is not equal

to $0.$

There is not sufficient sample evidence to support the claim that the mean difference of post$-$test

from pre$-$test is not equal to $0.$