Question

Using the set of scores below, determine if the difference between the two sets of scores is significant at alpha .05, two tailed.  Determine this through the paired t-test.  Show the 5 steps of hypothesis testing. Solve manually, by hand showing all steps. Do not use SPSS or excel.

X                     Y

            3                      8

            8                      7

            5                      6

            7                      7

            6                      6

            8                      9

Answer 1

At 5% level of significance we want to test the claim that if there is a significant difference between the two sets of scores.

The hypothesis testing problem is:

The data is

X	Y	d=X-Y	d^2
3	8	-5	25
8	7	1	1
5	6	-1	1
7	7	0	0
6	6	0	0
8	9	-1	1
	Total	-6	28

The mean of the difference is:

The standard deviation is:

The test statistic is:

Here degrees of freedom for the test are df=n-1=5

Therefore, the t critical value at 5% level of significance for two tailed test is:

        ### By using t table

Since the test statistic t=-1.27864>-2.571, We are unable to reject the null hypothesis.

Therefore, we don not have enough evidence to claim that there is a significant difference between the two sets of scores.