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Question 2 of 30

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M:C:MC:2

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SAT

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Problem Solving and Data Analysis

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A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology-degree program read per day?

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40 randomly selected undergraduate psychology-degree program students

Correct Answer: 
No

40 randomly selected undergraduate students from all degree programs at the college

Correct Answer: 
No

300 randomly selected undergraduate psychology-degree program students

Correct Answer: 
Yes

300 randomly selected undergraduate students from all degree programs at the college

Correct Answer: 
No

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Choice C is correct. Increasing the sample size while randomly selecting participants from the original population of interest will most likely result in a decrease in the margin of error.

Choice A is not the correct answer. This answer may result from a misunderstanding of the importance of sample size to a margin of error. The margin of error is likely to increase with a smaller sample size.

Choice B is not the correct answer. This answer may result from a misunderstanding of the importance of sample size and participant selection to a margin of error. The margin of error is likely to increase due to the smaller sample size. Also undergraduate students from all degree programs at the college is a different population than the original survey and therefore the impact to the mean and margin of error cannot be predicted.

Choice D is not the correct answer. Undergraduate students from all degree programs at the college is a different population than the original survey and therefore the impact to the mean and margin of error cannot be predicted.

Question Difficulty: 
easy
Objective: 

Students must first read and understand statistics calculated from a survey that was conducted. Then, students must use apply their knowledge about the relationship between sample size and subject selection on margin of error.