Matt and Diego suspect that people are more likely to agree to participate in a survey if the interviewers are dressed up. To test this idea, they went to the local grocery store to survey customers on two consecutive Saturday mornings at 10 A.M. On the first Saturday, they wore casual clothing (tank tops and jeans). On the second Saturday, they dressed in button-down shirts and nicer slacks. Each day, they asked every fifth person who walked into the store to participate in a survey. Their response variable was whether or not the person agreed to participate. Here are their results:

a. Calculate the difference (Casual – Nice) in the proportion of subjects that agreed to participate in the survey in the two groups.

b. Assume the study design is equivalent to randomly assigning shoppers to the “casual” or “nice” groups. A total of 100 trials of a simulation were performed to see what differences in proportions would occur due only to chance variation in this random assignment. Use the results of the simulation in the following dotplot to determine if the difference in proportions from part (a) is statistically significant. Explain your reasoning.

Transcribed Image Text:

Clothing Casual Nice Agreed 14 27 Participation Declined 36 23