Question

Use a t-distribution and the given matched pair sample results to complete the test of the given hypotheses. Assume the results come from random samples, and if the sample sizes are small, assume the underlying distribution of the differences is relatively normal. Assume that differences are computed using d=x1-x2.

Test H0 : μd=0 vs Ha : μd>0 using the paired data in the following table:

Situation 1	120	156	145	175	153	148	180	135	168	157
Situation 2	120	145	142	150	165	148	160	142	162	150

Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic =

p-value =

Answer 1

Situation 1	Situation 2	Difference
120	120	0
156	145	11
145	142	3
175	150	25
153	165	-12
148	148	0
180	160	20
135	142	-7
168	162	6
157	150	7
	Total	53

Sample size = n = 10

Sample mean of difference = = 5.3

Sample standard deviation of difference = = 11.3142

Test statistic is

Degrees of freedom = n - 1 = 10 - 1 = 9

P-value = P(T > 1.48) = 0.086