## Project A: Screentime Challenge

Students sometimes get a bad reputation for the amount of time they spend on their smartphones. But what about the screen times of faculty and staff? Do you think students really have higher screen time averages than the faculty and staff at their schools? This project will allow you to investigate this claim for yourself.

#### Step 1

For this project you will need
$30$ volunteers, with approximately half being students and half being faculty or staff. (It doesn't have to be exactly
$15$ each.) Ask each volunteer to look up *yesterday's* total screen time as recorded on their smartphone. It's important that the screen times recorded are all the same day of the week for consistency. It is also necessary to record a full day of screen time, which is why you cannot use the screen time for the current day, which would be incomplete. Keep your data organized in a chart.

#### Step 2

Divide the results into two groups, students and faculty/staff. Compute the mean and sample standard deviation of each group. Record your statistics below.

${n}_{\text{students}}=\overline{)\phantom{000000000}}$

${n}_{\text{faculty/staff}}=\overline{)\phantom{000000000}}$

${\stackrel{\_}{x}}_{\text{students}}=\overline{)\phantom{000000000}}$

${\stackrel{\_}{x}}_{\text{faculty/staff}}=\overline{)\phantom{000000000}}$

${s}_{\text{students}}=\overline{)\phantom{000000000}}$

${s}_{\text{faculty/staff}}=\overline{)\phantom{000000000}}$

#### Step 3

Construct a $95\%$ confidence interval for the true difference between the mean screen time of students and faculty/staff. Assume that the population variances are not the same and that the population distributions of screen times are approximately normal for both students and faculty/staff.

#### Step 4

Consider your results and write up your conclusion. Does your study show that students average more screen time than faculty and staff? Are your results convincing? Why or why not? Consider other factors such as how the sample was chosen, possible sources of bias, and the limits of interpreting the confidence interval when you make your conclusion.