You wish to test the following claim ( H a ) at a significance level of α = 0.01 . For the context of this problem, μ d = μ 2 − μ 1 where the first data set represents a pre-test and the second data set represents a post-test. H o : μ d = 0 H a : μ d ≠ 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 = 111 subjects. The average difference (post - pre) is ¯ d = 4.6 with a standard deviation of the differences of s d = 15.1 . 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.
Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) ≠ 0
Rejection Region
This is two tailed test, for α = 0.01 and df = 110
Critical value of t are -2.621 and 2.621.
Hence reject H0 if t < -2.621 or t > 2.621
Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (4.6 - 0)/(15.1/sqrt(111))
t = 3.210
P-value Approach
P-value = 0.0017
As P-value < 0.01, reject the null hypothesis.
The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
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