Jay-Z hypothesizes that exactly 40% of college students

are illegally downloading Dr. Dre's songs. A sample of 200 college students was taken. The

data Downloads.xlsx" presents the results with 1 indicating that a student is indeed illegally

downloading Dr. Dre's music. Mu= 0.32

a) For the given data, at the 0.05 level of significance, can we reject Jay-Z's (null) hypothesis?

b) For the given data, determine a 95% confidence interval for the proportion of college

students illegally downloading Dr. Dre's songs. (The Central Limit Theorem (CLT)

may be invoked here.)

The data in the Excel file were actually randomly generated using the following command

copied down 200 times: IF(RAND()<0.38,1,0). You are asked below to use this same command to perform a simulation.

c) For this simulation, what is the true proportion of college students illegally downloading

Dr. Dre's music?

d) Let the random variable X represent the sample mean. Given the simulation's true

proportion, determine the exact probability P(X = :40) (that is, the probability that

the sample mean exactly equals Jay-Z's hypothesized population mean). Do not invoke

the CLT here.

e) Simulation Exercise (submit Excel work): Use a Data Table to create simulation

of an experiment with 500 trials. The data presented in Downloads.xlsx" represents

one possible trial of the same experiment. Each trial then includes 200 samples of the

population of college students. You are being asked to generate 500 additional fresh

trials, with 200 samples each. For each trial, use the sample proportion to construct

a 95% confidence interval. Finally, report the fraction of the 500 trials (i) in which there is a Type I error and (ii) in which

there is a Type II error.