Question

Consumers Energy states that the average electric bill across the state is $67.16. You want to test the claim that the average bill amount is greater than $67.16. The hypotheses for this situation are Null Hypothesis: μ ≤ 67.16, Alternative Hypothesis: μ > 67.16. If the true statewide average bill is $51.28 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

a. Type I Error has occured.
b. No error has occured.
c. We do not know the degrees of freedom, so we cannot determine if an error has occured.
d. Type II Error has occured
e. We do not know the p-value, so we cannot determine if an error has occured.

Answer 1

B: No error has occured

Explanation:

In statistical hypothesis testing, we have two types of errors namely Type I error and Type II error.

Type I error occurs when we reject the null hypothesis although it is true. Meanwhile, Type II error occurs when we fail to reject the null hypothesis null hypothesis even though it is false.

Now, we are given the null and alternative hypothesis as;

Null Hypothesis: μ ≤ 67.16

Alternative Hypothesis: μ > 67.16.

Where μ represents the statewide average bill.

We are also given the true statewide average bill is $51.28.

Now, the true statewide average bill falls within the range of the null hypothesis given.

Thus, we can't reject the null hypothesis since it is true.

Now, we are told the null hypothesis is not rejected and that is correct.

Thus, there is no error as it doesn't fall into the type I or the type II error.