Question

Kibble Pet Plus believes that it has a market share of 32 percent of the local dog food market. They survey 100 dog owners and ask whether or not it is their regular source of dog food, and 27 people say "yes". Suppose a hypothesis test is made to see, whether Kibble Pet Plus's market share is different from 32%. In this context, committing a Type I error

a. occurs when they conclude that the percentage of customers using Kipple Pet Plus for their dog food is more than 32% when in fact it is less than that.
b. occurs when they conclude that the percentage of customers using Kipple Pet Plus for their dog food is 32% when in fact it is not.
c. occurs when they conclude that the percentage of customers using Kipple Pet Plus for their dog food is different from 32% when in fact it is not.
d. occurs when they conclude that the percentage of customers using Kipple Pet Plus for their dog food is less than 32% when in fact it greater than that.

Answer 1

A Type I error in the context of Kibble Pet Plus's market share hypothesis test would occur if they falsely conclude that their market share is different from 32% when it truly is 32%. This is known as a false positive.

Step-by-step explanation:

When Kibble Pet Plus performs a hypothesis test to determine if their market share is different from 32%, a Type I error would occur if they falsely conclude that the percentage of customers using Kibble Pet Plus as their regular dog food source is different from 32% when in fact it is 32%. Specifically, a Type I error in this scenario would be:

c. occurs when they conclude that the percentage of customers using Kibble Pet Plus for their dog food is different from 32% when in fact it is not.

This type of error represents a false positive; that is, the error of rejecting a true null hypothesis. Conversely, a Type II error would be the mistake of failing to reject a false null hypothesis, or a false negative. In other words, it occurs when the test does not detect a difference from 32% when there actually is one.