A recent survey of 200 randomly selected households showed that 8 had a single male as the head of household. Forty years ago, a survey of 200 randomly selected households showed that 6 had a single male as the head of household. At α = 0.05, can it be concluded that the proportion has changed? Find the 95% confidence interval of the difference of the two proportions. Does the confidence interval contain 0? Why is this important to know?

For each of these problems, perform the following steps.

a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.