Home / AP® Exam / AP® Statistics / 3.4 Potential Problems with Sampling – MCQs

AP Statistics 3.4 Potential Problems with Sampling - MCQs - Exam Style Questions

AP Statistics -MCQs and Answers - All Topics

Question

The American Academy of Pediatrics advises against feeding babies solid foods before they reach \(4\) months old. A research group obtains a simple random sample of \(5,000\) mothers nationwide and mails each one a survey asking questions about their feeding practices. Of the \(1,000\) mothers who completed the survey and mailed it back, \(40\%\) indicated that they started feeding their baby solid foods before age \(4\) months. A newspaper reports on the study with the headline, “Infants are Fed Solid Foods Too Soon.” Which of the following is the most serious concern regarding this study?
(A) There was no control group.
(B) There could be serious non-response bias.
(C) The sample size was too small.
(D) There was no random assignment.
(E) The sampling design did not incorporate stratification.
▶️ Answer/Explanation
Detailed solution

1. Analyze the Survey Method:
– A survey was sent to \(5,000\) randomly selected mothers.
– Only \(1,000\) mothers completed and returned the survey.
– This is a response rate of only \(20\%\) (\(\frac{1000}{5000}\)).

2. Identify the Potential Bias:
With such a low response rate (\(80\%\) did not respond), there is a very high risk of **non-response bias**. The \(1,000\) mothers who chose to respond may have systematically different feeding practices or opinions compared to the \(4,000\) who did not respond. Therefore, the sample of \(1,000\) is likely not representative of the intended population.
✅ Answer: (B)

Question

A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?
(A) The wording of the questions in the survey leads people to respond in a certain way.
(B) The behavior of the interviewer leads people to respond in a certain way.
(C) People might be uncomfortable with the survey questions and, as a result, might not always respond to those questions truthfully.
(D) Many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond.
(E) People without telephones are overlooked in the sampling procedure used to determine who is surveyed.
▶️ Answer/Explanation
Detailed solution

1. Define Nonresponse Bias:
Nonresponse bias occurs when individuals chosen for a sample are unable or unwilling to participate, and their views are systematically different from those who do participate. This skews the results because the responding group is not representative of the intended sample.

2. Analyze the Options:
– (A) is response bias (wording of question).
– (B) is response bias (interviewer effect).
– (C) is response bias (truthfulness).
– (E) is undercoverage bias.
– (D) perfectly describes the situation where the opinions of non-responders differ from responders, which is the definition of nonresponse bias.
✅ Answer: (D)

More AP Statistics MCQ Questions..
Scroll to Top