Question

Suppose that, in a population of middle-aged men, the average length of a male's forearm is 15 inches, with a standard deviation of 1.5 inches. However, we have reason to believe that this figure is false. So, we test a sample of 49 men and find that within this sample, we observe a mean of 16 inches.

a) Estimate a mean forearm length.

b) Conduct a hypothesis test with a null and alternative hypothesis.

Answer 1

Solution:

a) The estimated mean forearm length is:

b)The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Now, the p-value is:

Conclusion: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that the average length of a male's forearm is not 15 inches