Question

How Many Hours on a Computer? Exercise 1.24 introduces the dataset PASeniors which includes many variables on a sample of high school seniors in Pennsylvania. One of the variables is ComputerHours, which gives the number of hours the student spent on a computer during the previous week. In the sample, 447 students answered the question, and the sample mean was 16.740 hours with a standard deviation of 17.688. Find and interpret a 99% confidence interval for the mean number of hours per week that high school seniors in Pennsylvania spend on the computer.

a. 14.575 to 18.905
b. 12.342 to 21.109
c. 20.678 to 23.440
d. 15.867 to 17.219

Answer 1

To find the 99% confidence interval for the mean number of hours per week that high school seniors in Pennsylvania spend on the computer, we can use the formula: Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size). The correct answer is option a. 14.575 to 18.905.

Step-by-step explanation:

To find the 99% confidence interval for the mean number of hours per week that high school seniors in Pennsylvania spend on the computer, we can use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)

Plugging in the given values:

Confidence interval = 16.740 ± (2.576 * 17.688 / √447)

Calculating this, we get a 99% confidence interval of approximately 14.575 to 18.905.

Therefore, the correct answer is option a. 14.575 to 18.905.