Question

A physician employed by a large corporation believes that due to an increase in sedentary living in the past decade, middle-age men have become fatter. In 1970, the corporation measured the percentage of fat in their employees. For the middle-age men, the scores were normally distributed with a mean of 22%. To test her hypothesis, the physician measures the fat percentage in a random sample of 18 middle-age men currently employed by the corporation. The fat percentages found were as follows: 24, 40, 29, 32, 33, 25, 15, 22, 18, 25, 16, 27, 26, 18, 27, 19, 31, 24.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 22
Alternative Hypothesis, Ha: μ > 22

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (25.06 - 22)/(6.5302/sqrt(18))
t = 1.988

P-value Approach
P-value = 0.0316
As P-value < 0.05, reject the null hypothesis.

there is sufficient evidence to conclude that the middle-age men have become fatter