Question

12 multiple choice 1.43 points a professor was interested in determining the amount of time college students spend sleeping, per night. the professor randomly selects 40 college students and finds that the mean amount of sleep they receive per night is 7.6 hours with a standard deviation of 1.3 hours. identify the correct formula and/or calculator function that would be used to construct a confidence interval for the mean amount of sleep for college students. formula: $hat{p} pm z_{\frac{alpha}{2}} sqrt{\frac{hat{p}(1 - hat{p})}{n}}$ calculator function: 1-propzint formula: $lb = sqrt{\frac{(n - 1)s^2}{chi^2_{\frac{alpha}{2}}}}$ and $ub = sqrt{\frac{(n - 1)s^2}{chi^2_{1 - \frac{alpha}{2}}}}$ formula: $\bar{x} pm t_{\frac{alpha}{2}} cdot \frac{s}{sqrt{n}}$ calculator function: t-interval formula: $lb = \frac{(n - 1)s^2}{chi^2_{\frac{alpha}{2}}}$ and $ub = \frac{(n - 1)s^2}{chi^2_{1 - \frac{alpha}{2}}}$

Explanation:

Step1: Identify parameter type

The problem targets the population mean sleep time ($\mu$), not proportion or variance.

Step2: Check population standard deviation

Population standard deviation ($\sigma$) is unknown; sample standard deviation ($s=1.3$) is used.

Step3: Choose appropriate interval

For mean with unknown $\sigma$, use t-interval: $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$, calculator function T-Interval.

Answer:

Formula: $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$; Calculator Function: T-Interval