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?

Explanation / Answer

Solution:-

H0: Null hypothesis being that the person has a high willingness-to-pay.

HA : Alternative that the person has a low willingness-to-pay.

A Type 1 Error is a false positive -- i.e. you falsely reject the (true) null hypothesis.

Type I error in this context means that she concludes that the person has a low willingness-to-pay but in relaity the person has a high willingness-to-pay.

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