Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002. 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=14n=14 subjects. The average difference (post - pre) is ¯d=−13.2d¯=-13.2 with a standard deviation of the differences of sd=21.4sd=21.4.

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.

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Answer 1

This is two tailed test, for α = 0.002 and df = 13
Critical value of t are -3.852 and 3.852.
Hence reject H0 if t < -3.852 or t > 3.852

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (-13.2 - 0)/(21.4/sqrt(14))
t = -2.308

The test statistic is...not in the critical region

This test statistic leads to a decision to..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 not equal to 0