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A research assistant selected 7575 undergraduate students at random from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 7575 students, extbackslash{}“How many minutes per day do you typically spend reading? extbackslash{}” The mean reading time in the sample was 8989 minutes, and the margin of error for this estimate was 4.284.28 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?\newlineA) 4040 undergraduate psychology-degree program students selected at random\newlineB) 4040 undergraduate students selected at random from all degree programs at the university\newlineC) 300300 undergraduate psychology-degree program students selected at random\newlineD) 300300 undergraduate students selected at random from all degree programs at the university

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Q. A research assistant selected 7575 undergraduate students at random from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 7575 students, extbackslash{}“How many minutes per day do you typically spend reading? extbackslash{}” The mean reading time in the sample was 8989 minutes, and the margin of error for this estimate was 4.284.28 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?\newlineA) 4040 undergraduate psychology-degree program students selected at random\newlineB) 4040 undergraduate students selected at random from all degree programs at the university\newlineC) 300300 undergraduate psychology-degree program students selected at random\newlineD) 300300 undergraduate students selected at random from all degree programs at the university
  1. Understand Margin of Error Impact: Understand the impact of sample size on margin of error. The margin of error in estimating a mean decreases as the sample size increases, assuming the variability of the data remains constant.
  2. Compare Sample Sizes: Compare the sample sizes.\newlineOriginal sample size = 7575 students.\newlineOptions:\newlineA) 4040 students from the psychology program.\newlineB) 4040 students from all programs.\newlineC) 300300 students from the psychology program.\newlineD) 300300 students from all programs.
  3. Identify Largest Psychology Sample: Identify the largest sample size from the psychology program. Comparing options A and C, since C has more students (300300 vs. 4040) and is specific to the psychology program, it will likely result in a smaller margin of error.
  4. Confirm Relevance of Psychology: Confirm that focusing on the psychology program is relevant.\newlineSince the original study and the question focus on psychology students, maintaining this focus (as in options A and C) ensures relevance and comparability.

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