Question

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 that is an example of spurious correlation is the relationship between the winner of a major sports championship and the performance of a stock index in that year. The​ "indicator" states that when a team from a particular conference wins the​ championship, the stock index will increase in that year. Since the first championship was​ held, the indicator has been correct 44 out of 56 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 44 or more times in 56 years?

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

Answer 1

Answer:-

Given that:-

The indicator has been correct 44 out of 56 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.

Here ,it follows Binomial distribution. Since the following conditions.

1.The number of sample observations is finite and independent. That is ,n = 56

2.The probability of success is known . That is p = 0.50

Therefore, the probability mass unction as follows:

a) Find  the probability that the indicator would be correct 44 or more times in 56 years.

=0+0.00000206+.....+0+0

=0.00000206

b) The probability that the indicator would be correct 44or more than times in 56 years is 0.00000206. This probability is very small .Thus it can be concluded that the indicator is not much useful as it depends on a third hidden variable.