Question

You wish to test the following claim (H1H1) at a significance level of α=0.001α=0.001. For the context of this problem, d=x2−x1d=x2-x1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0Ho:μd=0
      H1:μd>0H1: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=148n=148 subjects. The average difference (post - pre) is ¯d=1.7d¯=1.7 with a standard deviation of the differences of sd=9.7.

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

Solution:

  H1:μd>0H1:μd>0

critical value for this test = 3.147

Test statistic = t

= 1.7 / 9.7 / 148

= 2.132

Test statistic = 2.132

The test statistic is not in the critical region .

fail to reject the null

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.