There were 12 first-round heats in the men’s 100-m race at the 1996 Atlanta Summer Olympics. Here are the reaction times in seconds (time to first movement) of the top four finishers of each heat. The...

There were 12 first-round heats in the men’s 100-m race at the 1996 Atlanta Summer Olympics. Here are the reaction times in seconds (time to first movement) of the top four finishers of each heat. The first 12 are the 12 winners, then the second-place finishers, and so on.

Because reaction time has little if any relationship to the order of finish, it is reasonable to view the times as coming from a single population.

a. Estimate the population mean in a way that conveys information about precision and reliability. [Note: Pxi = 8:08100; Px2 i = 1:37813:] Do the runners seem to react faster than the swimmers in Exercise 59?

b. Calculate a 95% confidence interval for the population proportion of reaction times that are below .15. Reaction times below .10 are regarded as false starts, meaning that the runner anticipates the starter’s gun, because such times are considered physically impossible. Linford Christie, who had a reaction time of .160 in placing second in his first-round heat, had two such false starts in the finals and was disqualified.