Question

An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected?

(A) Standard error of the mean increases, Width of confidence interval becomes wider.
(B) Standard error of the mean increases, width of confidence intervale becomes narrower.
(C) Standard error of the mean Decreases, width of confidence interval becomes wider.
(D) Standard error of the mean decreases, width of confidence interval becomes narrower.
(E) Cannot be determined.

Answer 1

(D) Standard error of the mean decreases, width of confidence interval becomes narrower.

Explanation:

Given that an analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year.

When all others remain constant n increases from 25 to 30

Because of this std error becomes
`(s)/(√(30) )`

instead of
`(s)/(√(25) )`

As a result standard error decreases and in turn margin of error also decreases.

Hence correct option would be

(D) Standard error of the mean decreases, width of confidence interval becomes narrower.