7 22 A triathlon consisting of swimming cycling and running

7 #22

A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. An article reports on a research study involving sixteen male triathletes. Maximum heart rate (beats/min) was recorded during performance of each of the three events. For swimming, the sample mean and sample standard deviation were 187.0 and 7.1, respectively. Assuming that the heart-rate distribution is (approximately) normal, construct a 98% CI for true mean heart rate of triathletes while swimming. (Round your answers to one decimal place.)

Solution

The degree of freedom =n-1=16-1=15

Given a=1-0.98 =0.02, t(0.01, df=15) =2.60 (from student t table)

So the lower bound is

xbar - t*s/vn=187 -2.60*7.1/sqrt(16) =182.4

So the upper bound is

xbar + t*s/vn =187 +2.60*7.1/sqrt(16) =191.6