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[Solved] Alpha Omega fraternity claims that the average grade point of their members is 3.1. To test this claim, the admissions office selects a random

Question: Alpha Omega fraternity claims that the average grade point of their members is 3.1.  To test this claim, the admissions office selects a random sample of 49 fraternity members and finds that their average grade point is 2.9 with a standard deviation of 0.25.

  1. Should the fraternity's claim be rejected at the 0.05 level of significance?
  2. Find the 95% confidence interval of the mean grade point for Alpha Omega members.
  3. Do the results of the hypothesis test and confidence interval concur?  Explain.

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