Question

You wish to test the following claim ($H_a$) at a significance level of $\alpha =0.002$. For the context of this problem, ${\mu }_d=PostTest-PreTest$ one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual.

      $H_o:{\mu }_d=0$
      $H_a:{\mu }_d\ne 0$

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-test	post-test
35.3	51.2
25.4	19.8
61.4	67.8
26	17.9
9.8	-1.7
45.7	42.5
43.3	42.6
45	67.7
41	37.4
42.3	24.3
35.7	-7.1
35.3	13.5
30	18.5
54	51.3
59.2	36
39.7	45.5
27.1	23.5

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?
p-value =  (Report answer accurate to 4 decimal places.)

The p-value is...

• less than (or equal to) $\alpha$

• greater than $\alpha$

• ${\displaystyle \mathrm{<br>}}$

This test statistic leads to a decision to...

• reject the null

• accept the null

• fail to reject the null

As 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.

Answer 1

There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0