Suppose that random samples of college freshman are selected from two universiti

Question

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 ??-4B estimates thedifferenceintestscores 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?

Explanation / Answer

1) The interpretation of the given confidence interval is that there is a 0.9 probability that the true population mean difference would lie in the given interval.

2) We can see that the given confidence interval also contain 0, therefore at 90% confidence level, we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the 2 means are different.

3) Here, the confidence interval does not contain 0, therefore we can conclude here that the test is significant at 90% confidence level, and therefore we have sufficient evidence here that the 2 means are not equal.

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