Question

Peggy constructed the 95 percent confidence interval (4.8,5.2) to estimate the slope of a regression model for a set of bivariate data with 24 data values. Peggy claims that the width of the confidence interval will increase if a sample size of 30 is used, all other things remaining the same. Quincy claims that the width of the confidence interval will decrease if a sample size of 30 is used. Which statement is true about the claims made by Peggy and Quincy?

Answer 1

Quincy's claim is correct.

Explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval decreases is the sample size increases, that is, if the sample size increases, the width of the interval decreases.

In this question:

Sample size of increases to 30 from 24, which means that the width of the interval will decrease.

Quincy's claim is correct.