Question

As we have seen, conducting a hypothesis test based on a sample of data is not a fail-safe endeavor. As managers we need to weigh the pros and cons of each type of error. The movie theater manager wants to test whether showing old classics changes the average satisfaction rating of his customers. The null hypothesis is that there is no change. Describe what the type I and type II errors would be in the context of this problem. Which would be worse for the theater manager: making a type I error or a type II error? Why?

Answer 1

Null hypothesis: No change in the average satisfaction

Alternative hypothesis : Change in the average satisfaction

Type 1 error says to reject a true null hypothesis

Type 2 error says to not reject a false null hypothesis.

In this context,

Type 1 error - when null hypothesis is true it means showing old classics does not change the average satisfaction rating of customers. But due to hypothesis testing manager came to a conclusion that old classics change average satisfaction. This is type 1 error in this case. In effect the manger would be showing old classics which in reality does not have any effect on average satisfaction level.

Type 2 error- In reality showing old classics change average satisfaction but due to hypothesis testing manager believes that it does not change average satisfaction. Here, the manager is committing type two error. In effect he would not show old classics to his customers. In this way he would not be able to change the average satisfaction of his customers.

Therefore, in conclusion one can say that theater manager would be worse if he commit type 2 error. He is not utilizing the opportunity of changing the average satisfaction of his customers which he could do in case of not doing type 2 error.