Question

In: Statistics and Probability

Use a t-distribution and the given matched pair sample results to complete the test of the...

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

Solutions

Expert Solution

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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