Question

Duke Energy reported that the cost of electricity for an efficient home in a particular neighborhood of Cincinnati, Ohio, was $104 per month.† A researcher believes that the cost of electricity for a comparable neighborhood in Chicago, Illinois, is higher. A sample of homes in this Chicago neighborhood will be taken and the sample mean monthly cost of electricity will be used to test the following null and alternative hypotheses.

H₀: μ ≤ 104

H_a: μ > 104

(A)

Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about the cost of electricity in the Chicago neighborhood?

a) Conclude that the population mean monthly cost of electricity in the Chicago neighborhood is not greater than $104 and hence is not higher than in the comparable neighborhood in b)   Cincinnati. Conclude that the population mean monthly cost of electricity in the Chicago neighborhood is greater than $104 and hence higher than in the comparable neighborhood in Cincinnati.

(b)

What is the type I error in this situation?

The type I error is rejecting H₀ when it is true.

The type I error is accepting H₀ when it is true.     

The type I error is rejecting H₀ when it is false.

The type I error is accepting H₀ when it is false.

What are the consequences of making this error?

This error occurs if the researcher concludes that the population mean monthly cost of electricity is greater than $104 in the Chicago neighborhood when the population mean cost is actually less than or equal to $104.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is less than or equal to $104 in the Chicago neighborhood when the population mean cost is less than or equal to $104.     

This error occurs if the researcher concludes that the population mean monthly cost of electricity is greater than $104 in the Chicago neighborhood when the population mean cost is greater than $104.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is less than or equal to $104 in the Chicago neighborhood when the population mean cost is actually greater than $104.

(c)

What is the type II error in this situation?

The type II error is rejecting H₀ when it is true.

The type II error is accepting H₀ when it is true.     

The type II error is rejecting H₀ when it is false.

The type II error is accepting H₀ when it is false.

What are the consequences of making this error?

This error occurs if the researcher concludes that the population mean monthly cost of electricity is greater than $104 in the Chicago neighborhood when the population mean cost is actually less than or equal to $104.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is less than or equal to $104 in the Chicago neighborhood when the population mean cost is less than or equal to $104.     

This error occurs if the researcher concludes that the population mean monthly cost of electricity is greater than $104 in the Chicago neighborhood when the population mean cost is greater than $104.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is less than or equal to $104 in the Chicago neighborhood when the population mean cost is actually greater than $104.

Answer 1

(A)

Since null hypothesis is rejected so we have evidence to support the alternative hypothesis.

That is correct option is:

Conclude that the population mean monthly cost of electricity in the Chicago neighborhood is greater than $104 and hence higher than in the comparable neighborhood in Cincinnati.

(b)

Type I is the probability of rejecting the true null hypothesis.

Correct options are:

The type I error is rejecting H₀ when it is true.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is greater than $104 in the Chicago neighborhood when the population mean cost is actually less than or equal to $104.

(c)

Type II is the probability of fail to reject the false null hypothesis.

Correct options are:

The type I error is rejecting H₀ when it is true.

This error occurs if the researcher concludes that the population mean monthly cost of electricity is less than or equal to $104 in the Chicago neighborhood when the population mean cost is actually greater than $104.