A triathlon consisting of swimming cycling and running is on

A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. The article “Cardiovascular and Thermal Response of Triathlon Performance” (Medicine and Science in Sports and Exercise, 1988: 385-389) reports on a research study involving nine 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 188.0 and 7.2, respectively. Assuming that the heart rate distribution is (approximately) normal, construct a 95% CI for true mean heart rate of triathletes while swimming.

Solution

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    188          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    7.2          
n = sample size =    9          
              
Thus,              
Margin of Error E =    4.703913563          
Lower bound =    183.2960864          
Upper bound =    192.7039136          
              
Thus, the confidence interval is              
              
(   183.3   ,   192.7   ) [ANSWER, B]