Suppose that your firm has only 2 types of customers: those with a high willingn

Question

Suppose that your firm has only 2 types of customers: those with a high willingness-to-pay and those with a low willingness-to-pay. A coworker from the marketing department claims that her algorithm can correctly identify whether a customer has a high willingness-to-pay or a low willingness-to-pay by the way the customer dresses. Suppose in actuality that she can correctly identify the high willingness-to-pay type 87% of the time, while 16% of the time she mistakenly identifies a low willingness-to-pay type as the high type. Presented with one customer and asked to identify whether this customer is either the high or low type, she considers her algorithms prediction to be a hypothesis test with the null hypothesis being that the person has a high willingness-to-pay and the alternative that the person has a low willingness-to-pay. What would be a Type I error in this context?

A) Predicting that the customer has a low willingness-to-pay when in fact the customer has a low willingness-to-pay.

B) Predicting that the customer has a low willingness-to-pay when in fact the customer has a high willingness-to-pay.

C) Predicting that the customer has a high willingness-to-pay when in fact the customer has a high willingness-to-pay.

D) Predicting that the customer has a high willingness-to-pay when in fact the customer has a low willingness-to-pay.

Explanation / Answer

Type 1 error is the rejection of null hypothesis when the null hypothesis is true.

So here predicting that customer has low willingness to pay when they have high willingness to pay, is a type 1 error.

B is correct.

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