Chapter 2, Problem 69CR

A mortgage lender routinely places advertisements in a local newspaper. The advertisements are of three different types: one focusing on low interest rates, one featuring low fees for first-time buyers, and one appealing to people who may want to refinance their homes. The lender would like to determine which advertisement format is most successful in attracting customers to call for more information.

1. a. Describe an experiment that would provide the information needed to make this determination. Be sure to consider extraneous variables, such as the day of the week that the advertisement appears in the paper, the section of the paper in which the advertisement appears, or daily fluctuations in the interest rate.
2. b. What role does random assignment play in your design?

To determine

Give a description of an experiment to determine the most attractive format of advertisement, while considering the extraneous variables, like, day of the week the advertisement appears, section of the paper in which it appears or fluctuations in interest rates on the daily basis.

Explanation of Solution

Answers may vary. One of the possible answers is given below:

The advertisements posted by a mortgage lender in a local newspaper are of three types: the first one focuses on low interest rates, the second one focuses on low fees for first-time buyers and the third one focuses on those willing to refinance their homes.

Suppose the local newspaper has s sections; the mortgage lender posts advertisements in d days of the week (d ≤ 7); there are 3 types of advertisements.

In order to identify the most attractive format for the people, the mortgage lender must post each of the 3 advertisements in every possible combination of days and sections. There are a total of sd combinations of days of the week and sections.

If the mortgage lender wants every advertisement format to appear exactly once for each combination, then there are 3sd newspaper issues required to carry out the experiment. If the mortgage lender wishes every advertisement format to appear r times, then 3rsd issues would be necessary to accommodate all the combinations.

The experiment can be performed by first selecting a particular combination of day of the week and section of the newspaper; in 3sd newspaper issues, every such combination appears 3 times; the 3 advertisement formats are randomly assigned to the three slots of the combination. This process is repeated, till each of the sd combinations receive all 3 advertisements.

The responses from each of these advertisement formats can now be compared.

A similar design can be constructed by incorporating the rates of fluctuations of the interest, which occur on the daily basis.

To determine

Explain the role of random assignment in the design.

Explanation of Solution

The advertisements are assigned randomly among the 3 issues having each combination. This ensures that that the advertisements are allocated evenly throughout the days of the week and over the 3 weeks. The random assignment also helps to avoid any personal bias from affecting the results of the study.