10.21

Use the data given and a 1% level of significance to test the following hypotheses. Assume the differences are normally distributed in the population.

 

            H₀: D = 0

            H_a: D > 0

 

Pair	Sample 1	Sample 2
1	38	22
2	27	28
3	30	21
4	41	38
5	36	38
6	38	26
7	33	19
8	35	31
9	44	35

Using:

 

 

 

 

With a one-tailed test, α = .01, , from table A.6.

 

If the observed test statistic,  is greater than , the null hypothesis will be rejected.

 

Pair	Sample 1	Sample 2	d
1	38	22	16
2	27	28	-1
3	30	21	9
4	41	38	3
5	36	38	-2
6	38	26	12
7	33	19	14
8	35	31	4
9	44	35	9

 

∑d = 64, 7.11, 6.45, α = .01, df = 9 – 1 = 8

 

 

= 3.31 is greater than =2.90, therefore the null hypothesis will be REJECTED.