Grades on a standardized test are known to have a mean of 1000 for students in t
ID: 1185481 • Letter: G
Question
Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students. b. With 5% significance level, Is there a statistical evidence that Queens College students perform differently than other students in the US? The same 453 students selected earlier are now given a two-hour tutoring session and then asked to take the test a second time. The average change in their test scores is 9 points, and the standard deviation of the change is 60 points. Assume the changes are from a Normal distribution. c. You are asked by the school administration to study whether students have performed better in their second attempt. State in terms of , the relevant null and alternative hypothesis in conducting this study. d. Compute the t statistic for testing against ; obtain the p- value for the test. e. Do you reject at the 5% level? At the 1% level? f. Provide a short summary of your conclusions from this study. Comment on the practical versus statistical significance of this estimate.Explanation / Answer
a. Construct a 95% confidence interval for the average test score for Florida students. A 95 % condence interval will be [(Florida mean) + 1:96 (Florida sd)/square root of n] = [1003:05; 1022:94]. ================================================ b. Is there statistically significant evidence that Florida students perform differently than other students in the United States? the National average 1000 is not included in the 95 % condence for Florida. ---- reject at the 5 percent level the hypothesis that the Florida students perform the same as the students from all over the nation.Related Questions
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