12
QuizMultiple Choice

Estimating the Mean Difference — Unit test

Question 12 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

A social worker at a large high school wants to estimate the number of days students are absent. He randomly selects 45 students and records the number of days each one is absent. The social worker constructs a 95% confidence interval for the true mean number of days students at this school are absent. Which of the following would decrease the margin of error?

Answer
A
using a sample of size 30
B
using a sample of size 40
C
constructing a 90% confidence interval
D
constructing a 99% confidence interval

Explanation

The margin of error gets smaller when the confidence level is lowered, because a lower confidence level uses a smaller critical value. Changing the sample size from 45 to 30 or 40 would increase the margin of error, since both are smaller samples. A 99% confidence interval would have a larger margin of error, so the 90% confidence interval decreases it.

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