Part I

Using simulation, you will generate samples of two test scores,score1,andscore2for 1,000 SAT test takers. Then you will compute the values ofmax,mean, andrecentfor each pair of scores. The resulting values ofmax,mean, andrecentwill be used to construct approximations to the sampling distributions of the three statistics, which will be referred to asmax2, mean2,andrecent2.

a.Using a tool of choice (Excel or R), obtain 1,000 sets of five "test scores" by generating observations from a normal distribution with mean 1200 and standard deviation 30. Explain how you generated the pairs.

b.Calculate the values ofmax2, mean2,andrecent2. Construct density diagrams for each.

Part II

Using simulation, you will generate samples of five test scores,score1, score2, score3, score4,andscore5for 1,000 SAT test takers. Then you will compute the values ofmax,mean, andrecentfor each quintuplet of scores. The resulting values ofmax5,mean5, andrecent5will be used to construct approximations to the sampling distributions of the three statistics.

a.Using a tool of choice, obtain 1,000 sets of five "test scores" by generating observations from a normal distribution with mean 1200 and standard deviation 30. Describe how you generated the quintuplets.

b.Calculate the values ofmax5, mean5,andrecent5. Construct density diagrams for each.

Part III

a.Explain how the sampling distributions ofmean2andmean5compare to what is expected based on the general properties of thex.

b.Based on the three distributions from Part I, for a two-time test taker, describe the advantage of using the maximum score compared to using either the average score or the most recent score.

c.Explain how the approximate sampling distributions of the maximum score for two-time and for five-time test takers compare.

d. Explain if a student who takes the exam five times has a big advantage over a student of equal ability who only takes the exam twice if the maximum score is used for college admission decisions.

Justify why you would recommend using the maximum test score, the average test score, or the most recent test score in making admission decisions