Question

A simple random sample of 50 adults is obtained, and each person’s height is measured.

The sample mean is 68 inches. The population standard deviation for heights is 2.35.

*Use a 0.01 significance level to test the claim that the sample is from a population

with a mean equal to 73, against the alternative hypothesis that the mean height

is NOT equal to 73. (ASSUME Normal). (5 points) If z0.01=−2.32 and z0.005=−2.57 are numbers s.t. P(Z < z0.01) = 0.01 and P(Z < z0.005) = 2.57.

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 73

H_a : 73

Test statistic = z

= ( - ) /    / n

= (68 - 73) / 2.35 / 50

Test statistic = -15.04

P-value = 0.000

Critical value = 2.57

| Test statistics | > Critical value

Reject the null hypothesis .