Question 236506: I can't figure out how to set the problem up. Can you please help? Thanks for all your help.
The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed. Test using = 0.10.
· State the null and alternate hypotheses
· Calculate the mean and standard deviation
· Determine which test statistic applies, and calculate it
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?
Before 56 38 56 33 38 51 57 55
After 56 38 64 37 43 55 63 61
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The pulse rates below were recorded over a 30-second time period, both before and after a physical fitness regimen. The data is shown below for 8 randomly selected participants. Is there sufficient evidence to conclude that a significant amount of improvement took place? Assume pulse rates are normally distributed. Test using = 0.10.
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Comment: "Improvement" would mean the after data is lower than the before
data for an individual subject.
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· State the null and alternate hypotheses
· Calculate the mean and standard deviation
· Determine which test statistic applies, and calculate it
· Determine the critical value(s).
· State your decision: Should the null hypothesis be rejected?
Before 56 38 56 33 38 51 57 55
After 56 38 64 37 43 55 63 61
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This is a before-after set of data. The data elements are dependent
because the before and after relate to the same subject (person) for
each pair.
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Subtract the after from its corresponding before to get a set of
differences (d's). Tha is the important data set.
Find the mean and std of that data set:
d-bar = -4.125 and s = 3.8504
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Ho: d = 0
H1: d < 0
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This type problem requires a t-test
Critical value:
t-value for one-tail test with alpha = 10% and df = 7 is -1.414
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test stat: t(-4.125 with df = 7) = -4.125/[3.8504/sqrt(8)] = -3.0301
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Conclusion: Since the test stat is in the reject interval,
reject Ho at the 10% significance level.
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Cheers,
Stan H.
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