Question

Suppose a random sample of 50 college students are asked to measure the length of their right foot in centimeters. A 95% confidence interval for the mean foot length for students at the college is found to be 21.709 to 25.091 cm. If a 99% confidence interval were calculated instead, how would it differ from the 95% confidence interval

Answer 1

A 99% confidence interval will be wider than a 95% confidence interval

Explanation:

From the question we are told that

The 95% confidence interval for for the mean foot length for students at the college is found to be 21.709 to 25.091 cm

Generally the width of a confidence interval is dependent on the margin of error.

Generally the margin of error is mathematically represented as

`E =  Z_{(\alpha )/(2) } * \sqrt{(\^ p (1- \^ p))/(n) }`

From the above equation we see that

`E \ \  \alpha \ \   Z_{(\alpha )/(2) }`

Here
`Z_{(\alpha )/(2) }` is the critical value of the half of the level of significance and this value increase as the confidence level increase

Now if a 99% confidence level is used , it then means that the value of

`Z_{(\alpha )/(2) }` will increase, this in turn will increase the margin of error and in turn this will increase the width of the confidence interval

Hence a 99% confidence interval will be wider than a 95% confidence interval