Question

You wish to test the following claim (H) at a significance level of a = 0.02. For the context of this problem, u = PostTest - Prel'est where the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your and are so that the differences are computed correctly.) Hd = 0 H: 70 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 72.1 34.9 83.9 74.3 63 75.6 106.1 38.3 70.1 47.1 63.4 73. 7 11.7 28.1 39.9 63.7 54.5 55.8 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.) The p-value is... less than (or equal to) a greater than a

Answer 1

The differences between Post Test and Pre Test is,

-37.2 -9.6 12.6 42.4 -24.4 -58.4 -64.7 -10.7 1.3 -39.9 -51.7 -45.6 -3.8 -11.7 1.3

Mean difference, d = -20.00667

Standard deviation of difference, sd = 29.56106

Standard error of mean difference , se = 29.56106 / $\sqrt{12}$ = 8.533543

Test statistic = (d - 0) / se = (-20.00667 - 0) / 8.533543 = -2.3445

Degree of freedom, df = n-1 = 12-1 = 11

For two tail test, p-value = 2 * P(t < -2.3445) = 0.0389

The p-value is greater than $\alpha$

Thus, we

fail to reject the null

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 not equal to 0.