Question

You wish to test the following claim ( H a ) at a significance level of α = 0.10 . 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 = 15 subjects. The average difference (post - pre) is ¯ d = − 15.1 with a standard deviation of the differences of s d = 41.8 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α 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 less than 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is less than 0. The sample data support the claim that the mean difference of post-test from pre-test is less than 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0

Answer 1

hypothesis:-

given data are:-

-15.1

standard deviation of differences () = 41.8

sample size (n) = 15

level of significance () = 0.10

so, our test statistic be:-

degrees of freedom= (n-1) = (15-1) = 14

p value = 0.0918 (using p value calculator, for t score = -1.399, df=14 , one sided test)

decision:-

p value = 0.0918 < 0.10 ( level of significance)

so, p value <

This test statistic leads to a decision to reject the null hypothesis.

As such, the final conclusion is that:-

There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is less than 0

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