Question

g A confidence interval was constructed using the sample standard deviation, say CI-1. We then construct a confidence interval with the same numerical values of sample mean, standard deviation, and sample size, but this time assuming the population standard deviation is known, say CI-2. The length of CI-2 is ________ the length of CI-1

Answer 1

Explanation:

Given that a confidence interval was constructed using the sample standard deviation, say CI-1.

We then construct a confidence interval with the same numerical values of sample mean, standard deviation, and sample size, but this time assuming the population standard deviation is known, say CI-2.

When population std dev is known we use std error =
`(\sigma)/(√(n) )`

For sample std deviation s, we use std error =
`(s)/(√(n) )`

When s= sigma, there will not be any difference between these two confidence intervals.

So answer is equal.