Question

A survey consisting of a sample of 463 first-year college students at a certain university asked, “About how many hours do you study during a typical week?” The mean response from the sample of students was 15.3 hours. Suppose we know that study times follow a Normal distribution with a standard deviation of 8.5 hours for all first-year students. Construct a 99% confidence interval for the mean study time of all first-year college students.

a. 14.28 ≤ � ≤ 16.32

b. 14.65 ≤ � ≤ 15.95

c. 14.53 ≤ � ≤ 16.07

d. −6.59 ≤ � ≤ 37.19

Solve the problem and show all your work below:

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 15.3

Population standard deviation =    = 8.5
Sample size = n =463

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

=2.576 * (8.5 / 463)

= 1.02

At 99% confidence interval mean is,

- E < < + E

15.3-1.02 < < 15.3+1.02

14.28 ≤ ≤ 16.32