Question

Test the claim that the paired sample data is from a population with a mean difference of 0. Assume the samples are random and dependent, and the populations are normally distributed. Use α = 0.05.

A 19 17 36 32 20

B 17 13 14 24 11

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) ≠ 0

Rejection Region
This is two tailed test, for α = 0.05 and df = 4
Critical value of t are -2.776 and 2.776.
Hence reject H0 if t < -2.776 or t > 2.776

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (9 - 0)/(7.8102/sqrt(5))
t = 2.577

P-value Approach
P-value = 0.0615
As P-value >= 0.05, fail to reject null hypothesis.