SAT Math Multiple Choice Question 412: Answer and Explanation

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Question: 412

7. In the United States, the original full retirement age was 65. The retirement age has since been pushed to 66 and will soon move to 67, as life expectancies go up. The Social Security Administration periodically conducts studies regarding retirement age. One such study focused on whether or not retiring early lowers a person's life expectancy. The study found a weak positive correlation between retirement age and life expectancy. If data from the study were graphed in a scatterplot, which of the following statements would be true?

  • A. The slope of the line of best fit would be a large positive number.
  • B. The slope of the line of best fit would be a negative number close to 0.
  • C. The data points would follow, but not closely, an increasing line of best fit.
  • D. The data points would be closely gathered around an increasing line of best fit.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: It's a good idea to get comfortable with the vocabulary used in statistics questions. Correlation simply means relationship. The word weak refers to the strength of the relationship, which has no effect on slope, but rather on how closely the data points follow the line of best fit.

Getting to the Answer: Be careful not to confuse slope and strength. Simply because a data set shows a weak correlation does not mean the slope will be close to zero. The data can still be gathered around a steep line of best fit. So, you can eliminate A and B. Also, keep in mind that the terms weak and positive are not related but rather are two independent descriptors of the correlation. So, the fact that the rate of change is positive has nothing to do with the strength of the correlation. In a weak correlation, the data points will follow the line of best fit, but not as closely as in a strong correlation, which means (C) is correct.

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