PSAT Math Multiple-Choice Question 397: Answer and Explanation

Question: 397

A polling company wanted to determine whether American voters would support a constitutional amendment that requires a person running for the U.S. Senate to have a minimum of a bachelor's degree. To do this, the company conducted a survey by sending 20,000 text messages across the entire United States to randomly selected phones with text-messaging capabilities. For every text that the company sent, it received a response to the survey. Which of the following best explains why this random sample is unlikely to be a representative sample of the American population's opinion in an actual election?

• A. The survey was biased because most Americans who own a cell phone have a bachelor's degree.
• B. Most Americans don't care about this issue, which is likely to skew the results.
• C. Surveys conducted via text messaging are illegal and as such are not considered reliable.
• D. There is no way to verify whether the respondents to the survey were U.S. citizens who were registered to vote.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Getting to the Answer: A good representative sample is not only random but also a good representation of the population in question. Here, the population in question is American voters. Choice (A) could be tempting because it might be true that cell phone owners are more educated, and more educated voters may prefer more educated senators, but not everyone with a cell phone is a registered voter. For example, minors, noncitizens, and citizens who aren't registered to vote are likely to make up at least a portion of the recipients of random texts sent out by the polling company. Since the survey is intended to sample voters, that is an important distinction. Thus, the inability to verify if the respondents were even registered to vote means that despite being randomly selected, the sample is unlikely to be a good representative sample. Choice (D) is correct.