CEOs revisited In Exercise 36 you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replacement) from the total annual compensations of the Fortune 800 CEOs. The summary statistics for these simulations were as follows: a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes? b) How close are the theoretical values to what was observed from the simulation? c) Looking at the histograms in Exercise 36, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution? d) What about the shape of the distribution of Total Compensation explains your answer in part c?

Conditional Probability: probability of an event, given that another event has occurred P(A| B) is the probability of A, given that B has occurred P(A| B) is not the same as P(B|A) If events are independent then P(A)=P(A|B) and P(B)=P(B|A) A contingency table (two way table) is a visual representation of the relationships between the variable. They make probabilities easier to figure out. Levels of the explanatory variables are the rows of the table and response variables are the columns Risk=Number in category/Total number in group We can use a contingency table to calculate Relative Risk= risk in category 1/ risk in category 2 Baseline risk Percent change in risk= (relative risk – 1) 100% Positive means risk increases Negative means risk decreases If relative risk is 1 then the