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 representing the National Football Conference wins the Super Bowl, the Dow Jones Industrial Average will increase in that year. When a team representing the American Football Conference wins the Super Bowl, the Dow Jones Industrial Average will decline in that year. Since the first Super Bowl was held in 1967 through 2009, the indicator has been correct 33 out of 43 times. 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 33 or more times in 43 years?
b. What does this tell you about the usefulness of this indicator?