) Grades on a standardized test are known to have a mean of 1000for students in the US. The test is administered to 453 randomlyselected students from Queens College, and they obtained an averagegrade of 1013 and a standard deviation of 108. a. Construct a 95 %confidence interval for the true average test score for QueensCollege students.(1pt) b. With 5% significance level, Is there astatistical evidence that Queens College students performdifferently than other students in the US?(1pt) From now, assumethe same 453 students selected earlier are now given a two-hourtutoring session and then asked to take the test a second time. Theaverage change in their test scores is 9 points, and the standarddeviation of the change is 60 points. Assume the changes are from aNormal ( , ) 2 ï ï³ distribution, and for every student, the changein score is the difference between the score after the tutoringsession, and the score before the tutoring session c. You are askedby the school administration to study whether students haveperformed better in their second attempt. State in terms of ï , therelevant null and alternative hypothesis in conducting thisstudy.d. Compute the t statistic for testing ?0 against ??; obtainthe p- value for the test.e. Do you reject ?0 at the 5% level? Atthe 1% level? f. Provide a short summary of your conclusions fromthis study. Comment on the practical versus statisticalsignificance of this estimate.
