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The miaa05 data set contains statistics on each of the 134 players in the MIAA 2005 Men's Basketball season. Choose 20 different random samples of size 15 from this data set. (The sample() function in R will automate the selection of samples; replicate() can be used to automate multiple samples.)

a) From each sample compute a 90% confidence interval for the mean PTSG (points per game) of MIAA players.

b) Of the 20 confidence intervals you computed in part a), how many actually did contain the true mean? (You can compute this since you know the population.)

c) How many of the 20 confidence intervals in part a) would you have expected (before you actually generated them) to contain the true mean?

d) In light of your answer in c), are you surprised by your answer in b)?

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