Question

Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is β, the probability of a Type II error in this scenario?

Answer 1

The Type II error is defined as the probability of not rejecting a null hypothesis, when the hypothesis is actually false.

In the case of this problem, this would be the probability of the store thinking that 70% or more of its clients shop only at their store, but the actual percentage of clients that don't shop at other store is lower.

Answer 2

See explanation

Explanation:

Given:

- H_0 : Claim that at least 70% of its customers do not shop at any other sporting goods stores

- H_1: less than 70% of its customers do not shop at any other sporting goods stores.

Find:

What is β, the probability of a Type II error in this scenario?

Solution:

- The type II Error is the probability of the Null hypothesis to be correct but in fact in reality the claim of Null hypothesis is wrong!

- In our case the type II error or the value of B would be:

Answer:

the probability that the sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores