Question

[adapted from Stock and Watson] (You may use a computer to make calculations, but to get full credit, you need to write out formulas and fill in the necessary information. Although LSAT scores are rounded to the nearest integer, for this assignment, round to the third decimal place.) Grades on LSAT are known to have a mean of 150 for students in the United States. The LSAT is administered to 65 randomly selected students at NYU. In this sample, the mean is 154 and the standard deviation is 10.

e. Conduct a hypothesis test of whether the prep course improves LSAT scores (among NYU students). Include all assumptions, the hypotheses, test statistic, and p-value, and interpret the result (including a conclusion). If you need to make an assumption to conduct a test, state the assumption, and conduct the test.

f. Use both part (d) and part (e) to answer the question: Is there statistically significant evidence that the prep course helped NYU students on the LSAT? Discuss how the hypothesis test and confidence interval are related or not.

g. The original 65 students are given the prep course and then are asked to take the LSAT a second time. The average change in their scores is +2 points, and the standard deviation of the change is 7 points. Construct a 95% confidence interval for the change in average LSAT scores.

h. Conduct a hypothesis test of whether NYU students will perform better on their second attempt on the LSAT after taking the prep course. Include all assumptions, the hypotheses, test statistic, and p-value, and interpret the result (including make a conclusion). If you need to make an assumption to conduct a test, state the assumption, and conduct the test.

i. Use both part (g) and part (h) to answer the question: Is there statistically significant evidence that NYU students will perform better on their second attempt on the LSAT after taking the prep course? Discuss how the hypothesis test and confidence interval are related or not.

j. Why do the statistical conclusions differ (or not) in parts (f) and (i) given they are both about change in average LSAT scores, considering the different changes and sample sizes?

Answer 1

here due to missing starting portion of question therefore part i can not be explained. but i am providing the formulas and all necessary calculations to calculate statistic, p value and some conclusions about simple hypothesis. hope you will understand well. if you have any querry please ask by comment i will respond to you and please give your good rating to answer for providing the best quality answers in future. thanks