Question

ch16 #13. (16.19) A class survey in a large class for first-year college students asked, "About how many hours do you study in a typical week?". The mean response of the 462 students was x⎯⎯hat = 14 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation 8 hours in the population of all first-year students at this university.

What is the 99% confidence interval (±±0.001) for the population mean?

Confidence interval is from _____ to ______hours.

Answer 1

Given that,

sample size (n) = 462

sample mean = 14 hours

Population standard deviation = 8 hours

Confidence level = 99% = 0.99

To find 99% confidence interval for population mean

A 99% confidence level has and has critical value

Z = 2.575

Confidence interval is,

Where,

Thus,

Therefore, 99% confidence interval for population mean is from 13.0416 to 14.9584 hours

Note:

1) Confidence interval upto three decimal places is,

(13.042, 14.958)

2) Confidence interval upto two decimal places is,

(13.04, 14.96)