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 253 students was x⎯⎯⎯ = 150 minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 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

Explanation:

Let X be the number of minutes the first year college students study on a typical weeknight.

Given that X is N(150, 65)

Sample size = n = 253

We have to find the 95% confidence interval

Std error of the sample =
`(\std dev)/(√(n) ) \\=(65)/(√(253) ) \\=4.087`

Since population std deviation is known we can use Z critical value

Z critical for 95% = ±1.96

Hence confidence interval = 150±1.96*4.087

=(141.90,158.10)