2. A researcher hypothesized that the pulse rates of long-distance athletes diff
ID: 2959227 • Letter: 2
Question
2. 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
e. Compute t obt
f. Should H0 be rejected? What should the researcher conclude?
Explanation / Answer
a. What statistical test should be used to analyze the data? Because the sample size is less than 30, the t-statistic should be used here instead of the z-statistic. ----------------------------------------------------------------------------------------- b. Is this a one- or two- tailed test? This is a one-tailed test. ----------------------------------------------------------------------------------------- c. What are H0 and Ha for this study? H0: µ = 60 Ha: µ < 60 (Claim) ----------------------------------------------------------------------------------------- d. Find tcv Assuming that the level of significance desired is 0.05, with 9 degrees of freedom, and a one-tailed test: t(critical) = -1.833 ----------------------------------------------------------------------------------------- e. Compute t obt Sample mean = (45 + 45 + 64 + 50 + 58 + 49 + 47 + 55 + 50 + 52)/10 = 51.5 Sample standard deviation = v[(45 – 51.5)2 + (45 – 51.5)2 + (64 – 51.5)2 + (50 – 51.5)2 + (58 – 51.5)2 + (49 – 51.5)2 + (47 – 51.5)2 + (55 – 51.5)2 + (50 – 51.5)2 + (52 – 51.5)2]/9 = 6.0231 t-observed = (51.5 – 60) / (6.0231 / v10) = -4.4627 ----------------------------------------------------------------------------------------- f. Should H0 be rejected? What should the researcher conclude? Since -4.4627 < -1.833, we reject H0. The researcher can conclude that there is sufficient evidence to support the claim that the long-distance athlete’s pulse ratesRelated Questions
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