63. There were 12 rst-round heats in the men s 100-

meter race at the 1996 Atlanta Summer Olympics.

Here are the reaction times in seconds (time to rst movement) of the top four nishers of each heat.

The rst 12 are the 12 winners, then the secondplace nishers, and so on.

1st .187 .152 .137 .175 .172 .165

.184 .185 .147 .189 .172 .156 2nd .168 .140 .214 .163 .202 .173 .175 .154 .160 .169 .148 .144 3rd .159 .145 .187 .222 .190 .158 .202 .162 .156 .141 .167 .155 4th .156 .164 .160 .145 .163 .170 .182 .187 .148 .183 .162 .186 Because reaction time has little if any relationship to the order of nish, 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: , .) Do the runners seem to react faster than the swimmers in Exercise 59?

b. Calculate a 95% con dence 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 rst-round heat, had two such false starts in the nals and was disquali ed.