# SOLUTION: 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 &#945; = .05 in a two-tailed test, does

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: 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 &#945; = .05 in a two-tailed test, does      Log On

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 Click here to see ALL problems on Probability-and-statistics 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(57384)   (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. --------------------------------------- (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 --- Critical Values for 2-tail T-test with alpha = 5%: +-invT(0.975 with df = 17) = +-2.1098 ------------------------- Test statistic: t(3.35) = (3.35-3.25)/[0.25/sqrt(18)] = 1.6971 ----- 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 ============================================================= (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 ------------------------------------------- (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. ================ Cheers, Stan H.