12.23 Does including a gift with a request for a donation affect the proportion who will make a donation?

This question was investigated in a study described in the report “Gift-Exchange in the Field” (Institute for the Study of Labor, 2007). In this study, letters were sent to a large number of potential donors in Germany. The letter requested a donation for funding schools in Bangladesh. Those who were to receive the letter were assigned at random to one of three groups. Those in the first group received the letter with no gift. Those in the second group received a letter that included a small gift (a postcard), and those in the third group received a letter with a larger gift (four postcards).

The response of interest was whether or not a letter resulted in a donation.

Donation No Donation No Gift 397 2865 Small Gift 465 2772 Large Gift 691 2656

a. Carry out a hypothesis test to determine if there is convincing evidence that the proportions in the two donation categories are not the same for all three types of requests. Use a significance level of .01.

b. Based on your analysis in Part

(a) and a comparison of observed and expected cell counts, write a brief description of how the proportion making a donation varies for the three types of request.