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: Treatment 1 15 12 14 21 15 11 14 22 Treatment 2 18 20 25 21 20 14 15 20

Answer 1

treatment 1	treatment 2
15	18	-3	0.390625
12	20	-8	19.14063
14	25	-11	54.39063
21	21	0	13.14063
15	20	-5	1.890625
11	14	-3	0.390625
14	15	-1	6.890625
22	20	2	31.64063
		sum=- 29	sum=127.875

sample size (n) = 8

hypothesis:-

test statistic be:-

df = (n-1) = (8-1 )= 7

p value be:-

[ in any blank cell of excel type =T.DIST(-2.399,7,TRUE) press enter]

decision:-

p value = 0.0238 <0.05 (Alpha)

so, we reject the null hypothesis.

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