Question

A study investigated if cell phone use impacted student drivers' reaction times. There were two groups: 27 students were assigned to the cell phone group while 27 students were assigned to the control group. The experiment measured the response time to traffic lights; for the cell phone group, the mean was 583 with a standard deviation of 89.5 and for the control group, the mean was 537.7 with a standard deviation of 66.5. Construct a 90% confidence interval for the difference in mean response times between the cell phone and control groups. What is the Margin of Error (E), Lower Limit, and Upper Limit?

Answer 1

In this study there are two groups one is cell phone group and other one is control group. The experiment conducted is used to measure the response time to traffic light for the cell phone group and control group. Let X and Y represents the response time to traffic light for cell phone and control group respectively with 27 students. Then

We have known standard deviation so we use by the method of z for obtaining the confidence interval

Then the confidence interval is given by

For 90% confidence interval with level of significance, = 10%=0.10. =1.645.

Therefore for given data we have confidence interval as

Therefore We have confidence interval as

Therefore the Lower limit of the confidence interval is 10.001 and upper limit of the confidence interval is 80.6.

Margin of Error is a statistics which express the amount of random sampling error which determines the width of the confidence interval. The margin of error for any is given by

Therefore for the given problem we have Margin of error as