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 less than 73. (ASSUME Normal). 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

H0: = 73

Ha: < 73

Test statistics

z = ( - ) / ( / sqrt(n))

= ( 68 - 73) / ( 2.35 / sqrt(50) )

= -15.04

From Z table,

z critical value at 0.01 significance level = -2.32

Since test statistics < -2.32 , Reject H0

We conclude that we have sufficient evidence to support the claim that the mean height is less than 73