Question

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. 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=117n=117 subjects. The average difference (post - pre) is ¯d=4d¯=4 with a standard deviation of the differences of sd=21.5sd=21.5.

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 test statistic is...

• in the critical region
• not in the critical region

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

The statistical software output for this problem is :

critical value = ± 1.658

Test statistics = 2.012

The test statistic is in the critical region .

reject the null

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.