Question 288027: At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.35 with a standard deviation of 0.25. (a) At α = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)? (b) Use the sample to construct a 95 percent confidence interval for the mean. Does the confidence interval include 3.25? (c) Explain how the hypothesis test and confidence interval are equivalent.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.35 with a standard deviation of 0.25.
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(a) At α = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)?
Ho: u = 3.25
Ha: u is not equal to 3.25
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Critical Values for 2-tail T-test with alpha = 5%:
+-invT(0.975 with df = 17) = +-2.1098
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Test statistic:
t(3.35) = (3.35-3.25)/[0.25/sqrt(18)] = 1.6971
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Conclusion: Since the ts is not in either reject interval
fail to reject Ho. The mean for the 18 students did not
differ significantly from 3.25
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(b) Use the sample to construct a 95 percent confidence interval for the mean. Does the confidence interval include 3.25?
sample mean: 3.35
standard error: 2.1098*0.25/sqrt(18) = 0.1243
95% CI: 3.35- 0.1243 < u < 3.35 + 0.1243
95% CI: 3.2257 < u < 3.4743
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(c) Explain how the hypothesis test and confidence interval are equivalent.
The CI establishes 2.1098*0.25/sqrt(18) interval to the right and
to the left of the sample mean.
The hypothesis test establishes a 2.1098*0.25/sqrt(18) interval
to the right and left of the hypothesized population mean.
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Cheers,
Stan H.
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