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=8n=8 subjects. The average difference (post - pre) is ¯d=5.2d¯=5.2 with a standard deviation of the differences of sd=6.7sd=6.7.

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

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: u : Mean of population Ho : P = 0 HAU>0 Hypothesis test results: Mean Sample Mean Std. Err. DF T-Stat 5.2 2.3688077 7 2.1951972 P-value 0.0321

Hence,

Critical value = 1.895

Test statistic = 2.195

The test statistic is in the critical region.

Reject the null

The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.