Question

For each of the following hypothesis testing scenarios, indicate whether or not the appropriate hypothesis test would be about a difference in population means. If not, explain why not. Scenario 1: The international polling organization Ipsos reported data from a survey of 2,000 randomly selected Canadians who carry debit cards (Canadian Account Habits Survey, July 24,2006 ). Participants in this survey were asked what they considered the minimum purchase amount for which it would be acceptable to use a debit card. You would like to determine if there is convincing evidence that the mean minimum purchase amount for which Canadians consider the use of a debit card to be acceptable is less than \(\$ 10\). Scenario 2: Each person in a random sample of 247 male working adults and a random sample of 253 female working adults living in Calgary, Canada, was asked how long, in minutes, his or her typical daily commute was ("Calgary Herald Traffic Study," Ipsos, September 17,2005 ). You would like to determine if there is convincing evidence that the mean commute times differ for male workers and female workers. Scenario 3: A hotel chain is interested in evaluating reservation processes. Guests can reserve a room using either a telephone system or an online system. Independent random samples of 80 guests who reserved a room by phone and 60 guests who reserved a room online were selected. Of those who reserved by phone, 57 reported that they were satisfied with the reservation process. Of those who reserved online, 50 reported that they were satisfied. You would like to determine if it reasonable to conclude that the proportion who are satisfied is higher for those who reserve a room online.

Short answer

Scenario 1: No, it's a test of a single population mean. Scenario 2: Yes, it's a test of a difference in population means. Scenario 3: No, it's a test of a difference in population proportions.

Step-by-step solution

Analyze Scenario 1

For the first scenario, it's not about differences in population means, but rather determining whether the mean of a single population is less than a certain value (\(\$10\)). So, it does not match a difference in population means hypothesis.

Analyze Scenario 2

In the second scenario, it is about the difference in the mean commute times for two populations (male workers and female workers). So, this matches the premise of a hypothesis test about a difference in population means.

Analyze Scenario 3

In the third scenario, the hypothesis being tested is whether there is a difference in proportions (guests satisfied with the telephone reservation process vs. guests satisfied with the online reservation process), not means. As such, this is not about a difference in population means.