Hello,

I'm struggling trying to find the answer for b. Do you know the answer and help would greatly be appreciated!



A clean air standard required that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop’s license if they find significant evidence that the shop is certifying vehicles that do not meet standards.

b) In this context, what is the Type II error?

Accept Ho, when Ho is wrong.

In this context, a Type II error refers to the situation where the state regulators fail to revoke the suspect repair shop's license even though there is sufficient evidence that the shop is certifying vehicles that do not meet the clean air standards.

To understand how to find the Type II error, we first need to understand the concepts of Type I and Type II errors in hypothesis testing:

1. Type I error (False Positive): This occurs when we reject the null hypothesis, even though it is true. In the given context, it would mean revoking the repair shop's license when they are actually certifying vehicles that meet the clean air standards.

2. Type II error (False Negative): This occurs when we fail to reject the null hypothesis, even though it is false. In the given context, it would mean not revoking the repair shop's license when they are actually certifying vehicles that do not meet the clean air standards.

To determine the Type II error in this context, we can consider the scenario in which the shop is indeed certifying vehicles that do not meet the clean air standards. If the state regulators fail to find significant evidence of this and do not revoke the shop's license, then it would be a Type II error.

It is important to note that the probability of making a Type II error depends on the specific hypothesis testing scenario, including factors such as sample size, significance level, and effect size.