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2. Suppose a new standardized test is given to 100 randomly selected third-grade students in New...

2. Suppose a new standardized test is given to 100 randomly selected third-grade students in New Jersey. The sample average score, Y¯ , on the test is 58 points, and the sample standard deviation, sY , is 8 points. (a) Construct a 95% confidence interval for the mean score of all New Jersey third graders.

(b) Suppose the same test is given to 200 randomly selected third graders in Iowa, producing a sample average of 62 points and a sample standard deviation of 11 points. Derive the formula for the sample variance of the difference in the sample means between New Jersey and Iowa.

(c) Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. Can you conclude that the population means for Iowa and New Jersey students are different?

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