A high school teacher discovers that her class this year did exceptionally bette

Question

A high school teacher discovers that her class this year did exceptionally better on an exam than classes in previous years had. She wishes to test the theory that this class is a higher performing cohort on average than previous cohorts. In particular her sample size is 50 students and her average this year on her first exam was an 85 percent. The long term average has been 60 percent.

(a) Propose a null and an alternate hypothesis for which she can test her assertion? (For ease with the next few parts you may assume at this point that the long term average is robust enough that she can treat it as a parameter)

(b) What is the p-value of the test results this year under the null distribution that you proposed? (You will want to convert the sample mean into something you know the distribution of. Then you will want to assume the null is true, to form a test statistic for your test, which you can evaluate against your known distribution)

(c) Define a rejection region of the null hypothesis for the average assuming a signicance level of .05 .

(d) Calculate the power of the test (You may assume that this year's average is the true value under the alternative to help you calculate the probability of rejection).

Explanation / Answer

a)

HO: p = 0.60

Ha: p > 0.6

b)

n =50 , p^ = 0.85

TS = (p^ - p)/(sqrt(pq/n)) = (0.85 - 0.6)/sqrt(0.6*0.4/50)

= 3.608439

p-value = P(Z > 3.608439) = 0.000154

c)

rejection region Z > 1.645

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