SAT Math Multiple Choice Question 750: Answer and Explanation

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Question: 750

15. A researcher is trying to estimate the daily amount of time undergraduate computer science majors spend on nonrecreational computer activities. She surveys 120 students from among the computer science majors at a large state university and asks them, "How much time do you spend in nonrecreational computer activities each day?" The mean of these responses is 210 minutes per day, with a standard deviation of 16.5 minutes. If another researcher wishes to present the same question to a new set of subjects at the same university, which of the following subject groups would most likely yield a data set with a smaller margin of error for the estimated daily amount of time undergraduate computer science majors spend on nonrecreational computer activities?

  • A. 240 randomly selected computer science majors
  • B. 240 randomly selected liberal arts majors
  • C. 80 randomly selected computer science majors
  • D. 80 randomly selected liberal art majors

Correct Answer: A

Explanation:

A

Data Analysis (data spread) HARD

One important rule in data gathering is, the more data we can gather on a population, the more reliable our statistics about that population will be. More specifically, the greater fraction of the population we can sample, the smaller our margin of error from the true value of the population statistic. Another important rule in data gathering is the more similar our sample is to the population of interest, the smaller our statistical error will be. Since the sample size is highest and the group is most like the population (of undergraduate computer science majors) in choice (A), that group should produce the smallest margin of error in the data.

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