Question

A consumer protection company is testing a seat belt to see how much force it can hold. The null hypothesis, H0, is that the seat belt can hold at least 5000 pounds of force. The alternative hypothesis, Ha, is that the seat belt can hold less than 5000 pounds of force.

a. What is a Type II error in this scenario?

Answer 1

When we conclude that the seat belt can hold atleast 5000 pounds of force but actually it can hold less than 5000 pounds of force.

Explanation:

We are given the following in the question:

The null and the alternate hypothesis are:

`H_(0): \mu \geq 5000\text{ pounds}\\H_A: \mu < 5000\text{ pounds}`

Type II error:

• It is the error of accepting a false null hypothesis.
• This is the false negative error.
• This is the error when we accept the null hypothesis but the null hypothesis is not true.

Thus, for the given scenario, we will make a type II error when we conclude that the seat belt can hold atleast 5000 pounds of force(non-reject the null hypothesis) but actually it can hold less than 5000 pounds of force(true alternate hypothesis).