Question

Pulse rate is an important measure of the fitness of a person's cardiovascular system. The mean pulse rate for American adult males is approximately 72 heart beats per minute. A random sample of 21 American adult males who jog at least 15 miles per week had a mean pulse rate of 52.6 beats per minute and a standard deviation of 3.22 beats per minute 4.

Answer 1

(a)

Here we have T52.6, s -3.22, n-21 Since populaiton SD is unknown so t critical value will be used. Level of significance: -0.01 Critical value: 2.845 Degree of freedom df -n-1-20 The requried confidence interval is: tt-52.6+ (3.22*2.845/sqrt(21) Nm 52.6+1.999 (50.601,54.599) Excel function for critical value: TINV(0.01,20) Hence, the required confidence interval is (50.601,54.599)

(b)

The distribution of pulse rate will be normally distributed.

(c)

The 90% confidence interval should be narrower because critical value will be small.

Here we have 52.6,s -3.22, n -21 Since populaiton SD is unknown so t critical value will be used. Level of significance: a Critical value: t 1.725 Degree of freedom: df -n-1-20 The requried confidence interval is: tt -52.6 (3.22*1.725/sqrt(21) -52.6+1.212 (51.388,53.812) Excel function for critical value: TINV(0.1,20) Hence, the required confidence interval is (51.388,53.812).

(d)

Yes this statement is correct. It shows that we can be 95% confident that true population mean lies in the above interval.

(e)

It is incorrect.

We cannot say that exactly 950 interval contains true average pulse rate but it is expected that 950 interval contains true average pulse rate.