Question: Explain whether you think the Rule for Sample Means applies to each of the following situations. If it does apply, specify the population of interest and the measurement of interest. If it does not apply, explain why not.

a. A researcher is interested in what the average cholesterol level would be if people restricted their fat intake to 30% of calories. He gets a group of patients who have had heart attacks to volunteer to participate, puts them on a restricted diet for a few months, and then measures their cholesterol.

b. A large corporation would like to know the average income of the spouses of its workers. Rather than go to the trouble to collect a random sample, they post someone at the exit of the building at 5 P.M. Everyone who leaves between 5 P.M. and 5:30 P.M. is asked to complete a short questionnaire on the issue; there are 70 responses.

c. A university wants to know the average income of its alumni. Staff members select a random sample of 200 alumni and mail them a questionnaire. They follow up with a phone call to those who do not respond within 30 days.

d. An automobile manufacturer wants to know the average price for which used cars of a particular model and year are selling in a certain state. They are able to obtain a list of buyers from the state motor vehicle division, from which they select a random sample of 20 buyers. They make every effort to find out what those people paid for the cars and are successful in doing so.