A research assistant selected 75 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 75 students, extbackslash{}“How many minutes per day do you typically spend reading? extbackslash{}” 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?A) 40 undergraduate psychology-degree program students selected at randomB) 40 undergraduate students selected at random from all degree programs at the universityC) 300 undergraduate psychology-degree program students selected at randomD) 300 undergraduate students selected at random from all degree programs at the university
Q. A research assistant selected 75 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 75 students, extbackslash{}“How many minutes per day do you typically spend reading? extbackslash{}” 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?A) 40 undergraduate psychology-degree program students selected at randomB) 40 undergraduate students selected at random from all degree programs at the universityC) 300 undergraduate psychology-degree program students selected at randomD) 300 undergraduate students selected at random from all degree programs at the university
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.
Compare Sample Sizes: Compare the sample sizes.Original sample size = 75 students.Options:A) 40 students from the psychology program.B) 40 students from all programs.C) 300 students from the psychology program.D) 300 students from all programs.
Identify Largest Psychology Sample: Identify the largest sample size from the psychology program. Comparing options A and C, since C has more students (300 vs. 40) and is specific to the psychology program, it will likely result in a smaller margin of error.
Confirm Relevance of Psychology: Confirm that focusing on the psychology program is relevant.Since 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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