Last name and acquisition timing. The speed with which consumers decide to purchase a product was investigated in the Journal of Consumer Research (Aug. 2011). The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names are earlier in the alphabet—called the last name effect. MBA students were offered up to four free tickets to attend a LO5 top-ranked women’s college basketball game for which there were a limited supply of tickets. The first letter of the last name of those who responded to an e-mail offer in time to receive the tickets was noted as well as the response time (measured in minutes). The researchers compared the response times for two groups of MBA students: (1) those with last names beginning with one of the first 9 letters of the alphabet and (2) those with last names beginning with one of the last 9 letters of the alphabet. Summary statistics for the two groups are provided in the table.
First 9 Letters: A–I Last 9 Letters: R–Z Sample size 25 25 Mean response time (minutes) 25.08 19.38 Standard deviation (minutes) 10.41 7.12 Source: Carlson, K. A., & Conrad, J. M. “The last name effect: How last name influences acquisition timing.” Journal of Consumer Research, Vol. 38, No. 2, Aug. 2011.

a. Construct a 95% confidence interval for the difference between the true mean response times for MBA students in the two groups.

b. Based on the interval, part

a, which group has the shortest mean response time? Does this result support the researchers’ last name effect theory? Explain.