tests involving paired differences

Question

You wish to test the following claim (HaHa) at a significance level of α=0.05. For the context of this problem, μd=μ2−μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0 

      Ha: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=7 subjects. The average difference (post - pre) is ¯d=−7.1 with a standard deviation of the differences of sd=5.9.

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 =

Answer 1

this is a left-sided test at alpha = 0.05 and n=7, so the critical t value is for 6 degrees of freedom and the negative of the 0.05 tail value for that DOF = -1.943

the test statistic is tcalc = DBAR/(STD DEV/SQRT(n) = -7,1 / (5.9/sqrt(7)) = -3.18

since tcalc < tcrit, you would reject the null hypothesis at alpha = 0.05