Question

Snappy dressers (4.2, 4.3) 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 dot plot to determine if the difference in proportions from part (a) is statistically significant. Explain your reasoning.

c. What flaw in the design of this experiment would prevent Matt and Diego from drawing a cause-and-effect conclusion about the impact of an interviewer’s attire on nonresponse in a survey?

Short answer

Part a) The required answer$-0.26$

Part b) Not statistically significant

Part c) The treatments were not randomly assigned to the subjects.

Step-by-step solution

Part a) Step 1: Given information

Given,

Part a) Step 2: Calculation

To begin, locate the column totals.

The count in the "Agreed" row of the table is then divided by the column total to get the proportion of subjects who are willing to participate.

Casual: $p_1=\frac{14}{50}=\frac{7}{25}=0.28$

Nice: $P_2=\frac{27}{50}=0.54$

When the proportions differ (Casual - Nice), the proportion of Casual is reduced by the proportion of Nice:

$P_1-P_2=0.28-0.54=-0.26$

Part b) Step 1: Calculation

Given,

The dots in the given dot plot represent the simulated difference in the proportion of people who agreed (Casual-Nice). In the dot plot, 0 is found in the middle of the majority of dots, indicating that a difference in proportions of $0$is likely to occur.

Despite the fact that 0 is likely to occur, the difference is not statistically significant. If $0$was not likely to occur, the difference would have been statistically significant.

Part c) Step 1: Calculation

When the effects of two variables on a response variable cannot be distinguished, they are said to be confounded.

Because the treatments were not arbitrarily assigned to the subjects, and they wore casual clothes one day and nice clothes the next, it was impossible to conclude that there was cause and effect in this case. As a result, the day they wore the clothes could have an impact on the results, and the day could not be distinguished from the treatments.