Question: One theory concerning the Dow Jones Industrial Average is that it is likely to increase during U.S. presidential election years. From 1964 through 2004, the Dow Jones Industrial Average increased in 9 of the 11 U.S. presidential election years. Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time.

a. What is the probability of the Dow Jones Industrial Average increasing in 9 or more of the 11 U.S. presidential election years if the true probability of an increase in the Dow Jones Industrial Average is 0.50?

b. Read Problem and note that the Dow Jones Industrial Average increased in 74% of the years studied. What is the probability of the Dow Jones Industrial Average increasing in 9 of the 11 U.S. presidential election years if the probability of an increase in the Dow Jones Industrial Average is 0.74?

Problem: Between 1872 and 2000, stock prices rose in 74% of the years (M. Hulbert, The Stock Market Must Rise in 2002? Think Again, The New York Times, December 6, 2001, Business, p. 6). Based on this information, and assuming a binomial distribution, what do you think the probability is that the stock market will rise

a. next year?

b. the year after next?

c. in four of the next five years?

d. in none of the next five years?

e. For this situation, what assumption of the binomial distribution might not be valid?