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) 1.645(3.20/6)
B) 1.645(10.24/6)
C) 1.96(3.20/6)
D) 1.96(10.24/6)

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) 1.645(3.20/6) 
B) 1.645(10.24/6) 
C) 1.96(3.20/6) 
D) 1.96(10.24/6)

Quizplus · Accepted Answer

When the sample size increases from 25 to 30, the standard error of the mean decreases because the denominator of the standard error formula (the square root of the sample size) increases. The width of the confidence interval is determined by the product of the critical value (either 1.645 or 1.96) and the standard error of the mean. Since the standard error decreases, the width of the confidence interval decreases as well. Therefore, we can choose the option that multiplies the reduced standard error by 1.96, which is choice C.

An Analyst Takes a Random Sample of 25 Firms in the Telecommunications