Question

Consumers Energy states that the average electric bill across the state is $98.15. You want to test the claim that the average bill amount is actually less than $98.15. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 98.15, Alternative Hypothesis: μ < 98.15. You complete a randomized survey throughout the state and perform a one-sample hypothesis test for the mean, which results in a p-value of 0.0218. What is the appropriate conclusion? Conclude at the 5% level of significance.

Answer 1

Answer:

We conclude that null hypothesis must be rejected at 5% level of significance.

Step-by-step explanation:

We are given that Consumers Energy states that the average electric bill across the state is $98.15. We want to test the claim that the average bill amount is actually less than $98.15.

For this we are given with the hypothesis situation as;

NULL HYPOTHESIS, $H_0$ : $\mu \geq$ 98.15

ALTERNATE HYPOTHESIS, $H_1$ : $\mu$ < 98.15

Also, level of significance is given as 5%.

Now, we are given with the P-value of the test statistics then our decision rule is given by;

• If P-value is less than the significance level, then we will reject our null hypothesis.

• If P-value is more than the significance level, then we will not reject our null hypothesis.

Since, according the question;

P-value = 0.0218 or 2.18%

Level of significance = 5%

Clearly, as we can see that P-value is less than the significance level, so we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the average bill amount is actually less than $98.15.