Question

A research organization wanted to estimate the average number of hours a college student sleeps per night during the school year. After randomly sampling 150 college students, the research organization determined the following 95% confidence interval: LaTeX: \left(7.1,7.5\right)( 7.1 , 7.5 ) hours per night.

Answer 1

The average number of hours slept per night during the school year by these 150 college​ students is 7.3 hours.

Explanation:

The (1 - α)% confidence interval for population mean (μ) is:

`CI=\bar x\pm z_(\alpha/2)* (\sigma)/(√(n))`

In this question we need to compute the average number of hours slept per night during the school year for these 150 college​ students.

To compute the value of the sample mean the formula is:

`\bar x=(UL+LL)/(2)`

Th 95% confidence interval for estimating the average number of hours a college student sleeps per night during the school year is:

CI = (7.1 hours, 7.5 hours)

Compute the value of sample mean as follows:

`\bar x=(UL+LL)/(2)`

`=(7.5+7.1)/(2)`

`=(14.6)/(2)`

`=7.3`

Thus, the average number of hours slept per night during the school year by these 150 college​ students is 7.3 hours.