Chapter 5, Problem 43PS

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 “indictor� 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 was held in 1967 through 2016, the indicator has been correct 38 out of 50 times. Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct $\text{50\%}$ of the time.

a. What is the probability that the indicator would be correct 38 or more times in 50 years?

b. What does this tell you about the usefulness of this indicator?