PSAT Math Multiple-Choice Question 658: Answer and Explanation

Question: 658

An amusement park researcher compiles data about the average height of ten-year-old children in a certain town to determine whether this age group will meet the minimum height requirements for a new attraction. The researcher selects 100 ten-year-old children at random from the town and finds that the average height has a 95% confidence interval between 42 and 48 inches. Which of the following conclusions could the researcher most reasonably make?

• A. There is a 5% chance that the average ten-year-old child in the town will have a height between 42 and 48 inches.
• B. It is very likely that the average ten-year-old child in the town will be less than 42 inches tall.
• C. It is very likely that the average ten-year-old child in the town will have a height between 42 and 48 inches.
• D. It is very likely that the average ten-year-old child in the town will not have a height between 42 and 48 inches.

Correct Answer: C

Explanation:

(C) A 95% confidence interval means that if the study is done at random many times, the average height statistically should fall between these two heights 95% of the time. In other words, choice (C) is correct. It is very likely that an average child will fall between these two heights.