Question

If you construct a 90% confidence interval for the population mean instead of a 95% confidence interval and the sample size is smaller for the 90%, but with everything else being the same, the confidence interval would: a. remain the same b. become narrower c. become wider d. cannot tell without further information.

Answer 1

Let the sample size for 90% confidence interval be and that of 95% confidence interval be .

Let's assume the standard deviation be .

So, the width of the 90% confidence interval = and the width of the 95% confidence interval = .

Given that, < . But again, < .

So, we can't conclude anything on the fact which interval is wider. We need further information.