Question

The Dean of Instruction at a local college requested that a new standardized test for an introductory statistics course be developed with the requirement that it should have µ = 120 points and σ = 15. A class of 30 students complete the new test with a mean grade of 115. Conduct a hypothesis test at α = .05 to determine whether the claim that µ = 120 can be supported. Use the p-value approach and complete the following to show how this would be done.

1.State the null and alternative hypotheses in words and in statistical symbols

2.What statistical test is appropriate to use? Explain the rationale for your answer

3.What is the value of the test statistic and the p-value of that outcome?

4.Interpret the outcome in terms of the original claim

5.What is unusual about this hypothesis test?

Answer 1

T=15 l=120 mean u=120 an nie. is + Given that, 0:30, X-115, 2=0.05 We want to test the claim that population . Hypothesis is given by Ho: The new standardized test for an introdu- ctory statistics course have 43120 points, Hii The new standardized test for introdu etory statistics course doesn't have 120 points U +1201 Test statistic given by Bu 115 - 120 &lrñ 151530 = -1.826 t test because sample size in 530) porale for t= -1.826 is p-value = 0.0781 Since, p-value > a level of significance find 0.078 >0.05) we fail to reject the null hypothesis, iil. The claim that The new standardized test for an introductory statistics course have lt=120 points is true at 220.05 level of 'significance. we use