A single sample is being used to construct a 90 confidence i

A single sample is being used to construct a 90% confidence interval for the population mean. What would be the difference between an interval for a sample of n = 25 and the interval for a sample of n = 100? Assume that all other factors are held constant.

a. With n = 100, the standard error would be larger and the interval would be wider.

b. With n = 100, the standard error would be larger and the interval would be narrower.

c. With n = 100, the standard error would be smaller and the interval would be wider.

d. With n = 100, the standard error would be smaller and the interval would be narrower.

Solution

When sample size increases, std error decreases.

Hence the margin of error decreases narrowing the confidence interval.

d. With n = 100, the standard error would be smaller and the interval would be narrower.