Suppose a 95% confidence interval for μ turns out to be (1,000,2,100).To make more useful inferences from the data,it is desired to reduce the width of the confidence interval.Which of the following will result in a reduced interval width?
A) Increase the population.
B) Increase the sample size.
C) Increase the confidence level.
D) Increase the sample mean.

Question

Quizplus · Accepted Answer

Increasing the sample size will decrease the width of the confidence interval while maintaining the same level of confidence. This is because larger sample sizes provide more precise estimates of the population parameter and decrease the standard error of the sample mean. Options A, C, and D do not affect the width of the confidence interval in the desired way. Increasing the population size (option A) may increase the standard error, resulting in wider intervals. Increasing the confidence level (option C) increases the level of certainty, but also results in wider intervals. Increasing the sample mean (option D) without changing the sample size or standard deviation does not affect the interval width.

Suppose a 95% Confidence Interval for μ Turns Out to Be