Question
In an article in the Journal of Marketing, Bayus studied the differences between "early replacement buyers" and "late replacement buyers" in making consumer durable good replacement purchases. Early replacement buyers are consumers who replace a product during the early part of its lifetime, while late replacement buyers make replacement purchases late in the product's lifetime. In particular, Bayus studied automobile replacement purchases. Consumers who traded in cars with ages of zero to three years and mileages of no more than 35,000 miles were classified as early replacement buyers. Consumers who traded in cars with ages of seven or more years and mileages of more than 73,000 miles were classified as late replacement buyers. Bayus compared the two groups of buyers with respect to demographic variables such as income, education, age, end so forth. He also compared the two groups with respect to the amount of search activity to the replacement purchase process. Variables compared included the number of dealers visited, the time spent gathering information, and the time spent visiting dealers. (a) 99 percent confident that x, the sample mean number of dealers visited, is within a margin of error of 04 of mu, the population mean number of dealers visited? n _______ buyers (b) 99.73 percent confident that x is within a margin of error of 05 of mu? n _______ buyers
Explanation / Answer
Here' how to solve the problems:
1.
Z = 2.56
Margin of error = .04
.04 = 2.56*.52/sqrt(n)
n = (2.56*.52/.04)^2 = 1107.558.
Rounding up -> 1108 is the sample size
2.
Z = 3
Margin of error = .05
.05 = 3*.52/sqrt(n)
n = (3*.52/.05)^2 = 973.44
Rounding up -> 973 is the sample size
