The authors of the paper “Driven to Distraction” (Psychological Science [2001]: 462–466) describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task, occasional red and green lights flashed on the computer screen. If a green light flashed, subjects were to continue driving, but if a red light flashed, subjects were to brake as quickly as possible and the reaction time (in msec) was recorded. The following summary statistics are based on a graph that appeared in the paper: n = 48 x 5 530 s = 70
a. Construct and interpret a 95% confidence interval for m, the mean time to react to a red light while talking on a cell phone. What assumption must be made in order to generalize this confidence interval to the population of all drivers?
b. Suppose that the researchers wanted to estimate the mean reaction time to within 5 msec with 95% confidence. Using the sample standard deviation from the study described as a preliminary estimate of the standard deviation of reaction times, compute the required sample size.