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# What's the deal with differences? No unread replies.No replies. Suppose that random samples of college freshman...

What's the deal with differences?

Suppose that random samples of college freshman are selected from two universities - 15 students from school A and 20 students from school B. On a standardized test:

• The sample from school A has an average score of 1000 with a standard deviation of 100.
• The sample from school B has an average score of 950 with a standard deviation of 90.

(Assume the test scores came from normal distributions in both schools.)

A 90% confidence interval for μ A − μ B estimates the difference in test scores at the two schools to be 50 ± 55.66.

1) Interpret the confidence interval in the context of this problem.

2) Based on this confidence interval, what conclusion would we reach if we tested the null hypothesis: "There is no difference in test scores between the two universities?" Explain.

3) Suppose a state official admitted that there was a typo in the report of the analysis done and that the 90% confidence interval was actually 50 ± 5.66. How would this impact your interpretation of the interval and the conclusion of the hypothesis test (in other words how would your answers to #1 and #2 change)?

The solution to this problem is given by

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