Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      Ha:μd<0Ha:μd<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=15n=15 subjects. The average difference (post - pre) is ¯d=−1.5d¯=-1.5 with a standard deviation of the differences of sd=6.3sd=6.3.

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

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

The p-value is...

• less than (or equal to) αα
• greater than αα

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 less than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0.
• The sample data support the claim that the mean difference of post-test from pre-test is less than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0.

Answer 1

Test Statistic :-

t = 2.198

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 2.198 ) = 0.9774
Reject null hypothesis if P value <    level of significance
P - value = 0.9774 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

The p-value is...greater than α

• fail to reject the null

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