Question

What's the deal with differences?

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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)?

Answer #1

The solution to this problem is given by

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