4
RCMultiple Choice

Unit Test — Cumulative exam

Question 4 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

A junior at a large high school wants to estimate the amount of time it takes to log in to a school computer. He randomly selects 35 students and records the amount of time it takes to log in. The junior constructs a 95% confidence interval for the true mean amount of time it takes to log in to a school computer. Which of the following would decrease the margin of error?

Answer
A
using a sample of size 20
B
using a sample of size 25
C
constructing a 90% confidence interval
D
constructing a 99% confidence interval

Explanation

A confidence interval’s margin of error gets smaller when the confidence level is lowered, because the interval needs to cover fewer possible values with certainty. Changing to a sample of 20 or 25 students would also increase the margin of error, since both are smaller than the original sample of 35. A 99% confidence interval would require a larger margin of error, so constructing a 90% confidence interval decreases it.

AI-written and checked against the verified answer.

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