Question

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (25.53, 37.87) and (23.59, 39.81). One of these intervals is a 99% CI and the other is a 95% CI. Please match them.

Answer 1

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI

Explanation:

The margin of error of a confidence interval is given by:

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.

In this question:

The narrower C.I. is the 95%, and the wider is the 99%. So

(25.53, 37.87): 95% CI

(23.59, 39.81): 99% CI