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Question: national average act score for high school students stands at...

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National average ACT score for high school students stands at 25. A teacher thinks that her students perform better than average. So she collects data for 32 students and finds out that their average is 26.5 with standard deviation 3.7.

(a) Set up a hypothesis test to see whether the teacher is right

(b) Construct a 95% confidence interval for the mean ACT score. Explain your choice of distribution in constructing the confidence interval (normal or t-distribution).

(c) Find the p-value for the test. What is your decision on the teacher’s claim?

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