Question

8) In a recent study of 500 randomly selected statistics students, students were asked the number of hours per week they spend studying for their statistics class. The results were used to compute confidence intervals for the population mean hours per week spent studying. The 90% confidence interval was (7.7, 8.3). What is the sample mean hours per week spent studying for the 500 randomly selected students? Show all work and explain how you determined your answer.

Answer 1

The sample mean hours per week spent studying for the 500 randomly selected students is 8 hours, which is the average between both bounds of the confidence interval.

Explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the sample mean is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 7.7

Upper bound: 8.3

(7.7 + 8.3)/2 = 8

The sample mean hours per week spent studying for the 500 randomly selected students is 8 hours, which is the average between both bounds of the confidence interval.