Marvin would like to answer the following question:
In Houston, do restaurants with drive-thru service have more health code violations, on average, than restaurants without drive-thru service?
Which of the following study designs would help Marvin answer his question?
(A) Select restaurants at random and use random assignment to divide them into two groups (with and without drive-thru service). Use health department records to determine the number of violations over the past 12 months.
(B) Select a random sample of restaurants with drive-through service and a random sample of restaurants without drive-through service. Use health department records to determine the number of violations over the past 12 months.
(C) Ask restaurant owners to volunteer to complete a survey. Collect data on their responses to these questions: (1) Does your restaurant have drive-thru service? (2) How many health code violations have you had over the past 12 months?
(D) Select restaurants at random and divide them into two groups (with and without health code violations). Count the number of restaurants in each group that offered drive-thru service over the past 12 months.
Standards
7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
S-IC.3: Recognize the purposes of and di"erences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Correct answer and commentary
Student performance
This question asks students to determine which of four proposed study designs is most appropriate for answering Marvin’s question. It is important to realize that the statistical question in this problem does not seek to determine if offering drive-thru service causes more health code violations than non-drive-thru restaurants. What is required is for test takers to determine if the two types of restaurants have different numbers of violations, on average.
The correct answer is option (B). In this option, two random samples are taken (whether or not the sample sizes are equal does not matter) and an authoritative source is used to determine the number of health code violations for each. The use of random samples will allow the results to be generalized to the populations of Houston restaurants offering and not offering drive-thru service.
Option (A) is not reasonable because Marvin cannot choose which restaurants will have drive-thrus and which will not; this is a characteristic of experiments and not observational studies.
Option (C) is not correct because in general, a survey may be a reasonable choice for an observational study, though care must be taken to ensure that the respondents to the survey are representative of the population of interest. In this case, because generalization to all Houston-area restaurants is desired, a volunteer survey will likely not result in an appropriate sample. Moreover, because health code violations are not socially desirable, it is likely that at least a few respondents may not correctly report the number of violations they received, thus compromising the data in another way.
Finally, option (D) is not correct because raw counts are compared rather than relative frequencies/proportions. Even if relative frequencies or proportions were used, Marvin wishes to compare averages which cannot be calculated in this design. This design might allow one to say whether restaurants offering drive-thru service represent a greater proportion of the restaurants that received health code violations than those not offering drive-thru service, but this is still not quite the best use of the two-way table. Instead, calculating the proportion of drive-thrus and non-drive-thrus with health code violations (i.e. grouping on the other variable) would be better.