Answer to Question #1560 in Statistics and Probability for ldavis

Question

& A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.
a. What statistical test should be used to analyze the data?

b. Is this a one- or two- tailed test?

c. What are H0 and Ha for this study?

d. Find tcv from appendix A in Jackson’s text.

e. Compute t obt

f. Should H0 be rejected? What should the researcher conclude?

Answer 1

a. t-test must be used , due to unknown variance.


b. This is a one tailed test.


c. H0: m<60;

& & Ha: m>=60



d. Tcv=-1.833 (n=10-1=9, with 0.95 confidence level )


e.

Mn=51.5

M=60, Sn=6.023

Tobt=sqrt(n)(Mn-M)/Sn=-4.462


f.Yes, we accept the hypothesis, because tobt<tcv. And the conslusion
is that runners’ pulses would be slower than of other athletes.