Question

The mean price of mid-sized cars in a region is $\$32000$. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

Short answer

Type I error: The mean price of mid-sized automobiles is $\$32,000$, when it is $\$32,000$.

Type II error: The average price of a mid-sized car is not $\$32,000$, whereas it is actually $\$32,000$.

Step-by-step solution

Given information

The mean price of mid-sized cars in a region is$\$32000$.

Explanation

There are four possible results when running a hypothesis test, based on the veracity (or falseness) of the null hypothesis $H_0$and the decision to reject or not.

1. When $H_0$is true, the decision is not to reject it.

2. If $H_0$is true, the decision is to reject it.

3. The decision is to not reject $H_0$even though it is false.

4. If $H_0$is untrue, the decision is to reject it.

Type I error: The mean price of mid-sized automobiles is $\$32000$, when it is $\$32,000$.

Type II error: The average price of a mid-sized car is not role="math" localid="1653549384021" $\$32,000$, whereas it is actually role="math" localid="1653549390631" $\$32,000$.