Question

Confidence Interval 1

All of the questions with the header "Confidence Interval 1" are based on the data in this problem.

A researcher at the Annenberg School of Communication is interested in studying the use of smartphones among young adults. She wants to know the average amount of time that college students in the United States hold a smartphone in their hand each day. The researcher obtains data for one day from a random sample of 25 college students (who own smartphones). She installs an app that registers whenever the smartphone is being held and the screen is on. The sample mean is 230 minutes, with a standard deviation of 11 minutes.

What is the 95% confidence interval for average daily time a smartphone is used among college students?

Please show all work for this question on your own sheet of paper. Take your time and organize it neatly with plenty of space. You will upload your work at the end. For some questions, just enter your answer in Canvas.

1. What value of t is used in the confidence interval?

2. What is the standard error?

3. What is the lower bound of the confidence interval?   

4. What is the upper bound of the confidence interval?

Answer 1

1)

Level of Significance ,    α =    0.05  
degree of freedom=   DF=n-1=   24  
't value='   tα/2=   2.0639    [Excel formula =t.inv(α/2,df) ]

2)

Standard Error , SE = s/√n =   11.000   / √   25   =   2.20

3)

margin of error , E=t*SE =   2.0639   *   2.200   =   4.541
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    230.00   -   4.541   =   225.4594

4)

Interval Upper Limit = x̅ + E =    230.00   -   4.541   =   234.5406

95%   confidence interval is (   225.46   < µ <   234.54   )