Question

Several states are considering legislation that would limit the use of cell phones while driving an automobile. A researcher at the University of Utah investigated whether cell phone use impairs drivers’ reaction times. Sixty-four randomly selected students were divided evenly into a treatment group and a control group. Participants were instructed to press a break button on a driving simulator when a red light flashed. The control, or ” no phone”, group listened to the radio while they performed the simulated driving. The treatment, or ”phone”, group carried out a conversation on the cell phone with someone in the next room. Each participant’s mean response time in tenths of seconds was recorded. Summary statistics of the data appear below.

Phone n1 = 31 X1 = 10.8 s1 = 5.8

No Phone n2 = 33 X2 = 5.5 s2 = 2.4

(a) (2 points) Should you use the pooled procedure or unpooled procedure? Why?

(b) (1 points) If you use the unpooled procedure what is the value of the degrees of freedom?

(c) (4 points) Compute a 95% confidence interval for the difference in response times between the two groups using the method you specified in (a). Use phone - no phone. Round the endpoints of the confidence interval to two decimal places.

(d) (2 points) Write a sentence interpreting your interval from part (a). Be specific about the meaning in context.

(e) (2 points) Does this confidence interval suggest that the mean reaction times differ? If so, which group has a slower reaction time? Why or why not?

Answer 1

(a) We should use the unpooled procedure, because here, one sample standard deviation is more than twice the other sample standard deviation.



(d) We are 95% confident that the difference in response times between the two groups (Phone and No Phone) will lie between 3.03 and 7.57 tenths of a second.

(e) Yes, the confidence interval suggests that the mean reaction times differ because the interval does not contain zero. The "No Phone" group has a slower reaction time. This can be judged from the fact that the confidence interval lies on the positive side of zero on the number line.