Question

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 285 students was x⎯⎯⎯x¯ = 132 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σσ = 65 minutes in the population of all first-year students at this university.

Use the survey result to give a 95% confidence interval for the mean study time of all first-year students.

Answer 1

Solution :

Given that,

Z_/2 = 1.96

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

= 1.96 * (65 / 285)

= 7.55

At 95% confidence interval estimate of the population mean is,

- E < < + E

132 - 7.55 < < 132 + 7.55

124.45 < < 139.55

(124.45 , 139.55)