Question

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 sample size.
B. Decrease the confidence level.
C. Both increase the sample size and decrease the confidence level.
D. Both increase the confidence level and decrease the sample size.

Answer 1

A. Increase sample size

Explanation:

From the formula for estimating the confidence level interval for the mean:

X - Z × s/sqrt n where; X = sample mean; Z = z value corresponding to 95%;

s = standard deviation and n = sample size

It is evident from the equation that the confidence interval for the mean is inversely proportional to the sample size (n), hence increasing the sample size will result in a reduced interval width.