Question

You wish to test the following claim ( H a ) at a significance level of α = 0.005 . For the context of this problem, μ d = P o s t T e s t − P r e T e s t one data set represents a pre-test and the other data set represents a post-test. Each row represents the pre and post test scores for an individual.

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 the following sample of data: pre-test post-test 68.7 67.5 41.6 56.6 57.4 61.7 51.3 60.4 80.1 84.1 67.4 66.2 65.4 87.5 78.4 92.8 72.1 79.7 61.1 75.5 50.3 60.6 45.1 32.8 36.7 66.7 66.6 53.7 76.9 70.8 48.9 71 45.1 15.1 47.4 40.9 60 63.6

What is the test statistic for this sample? test statistic = _______(Report answer accurate to 4 decimal places.)

What is the p-value for this sample? p-value = ______ (Report answer accurate to 4 decimal places.)

Answer 1

Hypothesis : μ d = Post Test − Pre Test

                     Ho : μd = 0     vs   Ha : μd ≠ 0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. So here we find difference and use one sample t test .

t test statistics formula is as ,

Here ,    ,     ,   , n = 19

Plug these values informula ,

Here alternative hypothesis contains , " " sign so test is two tailed test .

And here df = n -1 = 19 - 1 = 18 .

To find p- value use excel command as , =TDIST(x value , df, tailes)  

If you plug values command is as , =TDIST(1.3894,18,2) then hit enter , so p-value = 0.1817.

Decision : P- value =0.1817 > significance level of α = 0.005 ; since fail to reject H0.

Conclusion : 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.