Question

Ages of students: A simple random sample of 100 U.S. college students had a mean age of 22.68 years. Assume the population standard deviation is σ = 4.74 years. Construct a 99% confidence interval for the mean age of U.S. college students.

The answer I posted my instructor says it is wrong. I came up with 21.45 to 23.91 a 99% confidence interval for the mean of the U.S college students

She said the z procedures are needed.

Thanks.

Answer 1

Solution :

Given that,

Sample size = n = 100

Z_/2 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.756 * (4.74 / 100)

= 1.22

At 99% confidence interval estimate of the population mean is,

- E < < + E

22.68 - 1.22 < < 22.68 + 1.22

21.46 < < 23.90

A 99% confidence interval for the mean : (21.46 , 23.90)