Question

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 twenty-five 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 189.0 and 7.3, 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.) , beats/min

Answer 1

Confidence interval (CI) mean upper (+) and lower (-) value of z(s/square root of n)

CI + / -  z(s/square root of n)

As we known that at 98% CI the z value is 2.054 (see attached tables)

therefore  

189 + / - 2.054 (7.3 / square root (9) )

189 + / - 2.054 (2.433)

189 + / - 4.997  

Therefore

CI= 189 – 4.997 OR  189 + 4.997

OR

CI= 184.003 to 193.997

According to the question’s requirement CI round to 1 decimal

CI= 184.0 to 194.0