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Answer to Question #1039 in Statistics and Probability for Faith Hood

Question #1039
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?
Expert's answer
a. We should use t-statistic test.
b. It's two tailed test
c. Ho : the avegage of the sample equals to the population mean
Ha : the avegage of the sample doesn't equal to the population mean
d. t(cv for df = 9 alpha = 0.05) = 2.26
e. t = (x-mean) / SE
mean = 51.5, SE = dev/√n = 6.23/√10 = 1.9
t = 4.46
f. As tobt > tcv the null hypothesis shouldn't be rejected.

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