Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized stock market indicator in the United States that is an example of spurious correlation is the relationship between the winner of the National Football League Super Bowl and the performance of the Dow Jones Industrial Average in that year. The "indicator" states that when a team that existed before the National Football League merged with the American Football League wins the Super Bowl, the Dow Jones Industrial Average will increase in that year. (Of course, any correlation between these is spurious, as one thing has absolutely nothing to do with the other.) Since the first Super Bowl held in 1967 through 2010, the indicator has been correct 35 out of 44 times (data extracted from W. Power, "The Bulls Want Jets Grounded," The Wall Street Journal, January 22, 2011, p. B2). 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 that the indicator would be correct 35 or more times in 44 years?
b. What does this tell you about the usefulness of this indicator?