Question

Researchers investigated the speed with which consumers decide to purchase a product. 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 begin with letters earlier in the alphabet - called the last name effect. MBA students were offered tickets to a basketball game. The first letter of the last name of respondents and their response times were noted. The researchers compared the response times for two​ groups: (1) those with last names beginning with a​ letter, A-​I, and​ (2) those with last names beginning a​ letter, R-Z. Summary statistics for the two groups are provided in the accompanying table. Complete parts a and b below. Sample Size A-I: 18 R-Z: 18 Mean Response Time (Minutes) A-I: 23.26 R-Z: 16.82 Standard Deviation (Minutes) A-I: 9.87 R-Z: 8.49

A. Construct a 90% 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 shorter mean response time? Does this result support the researchers' last name effect theory? Explain.

Answer 1

(a) The 90% Confidence Interval for the difference between the true mean response times for MBA students in the two groups is between 1.25 and 11.63.

1	2
23.26	16.82	mean
9.87	8.49	std. dev.
18	18	n
	34	df
	6.44	difference (1 - 2)
	84.75	pooled variance
	9.21	pooled std. dev.
	3.07	standard error of difference
	1.25	confidence interval 90.% lower
	11.63	confidence interval 90.% upper
	5.19	margin of error

(b) Since the confidence interval is positive, we can say that the R-Z group has a shorter mean response time. Yes, this result support the researchers' last name effect theory that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names begin with letters earlier in the alphabet - called the last name effect because the confidence interval is positive and does not contain 0.