Question

1. 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 73
Alternative Hypothesis, Ha: μ ≠ 73

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (68 - 73)/(2.35/sqrt(50))
z = -15.04

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.