Duke Energy reported that the cost of electricity for an efficient home in a par

Question

Duke Energy reported that the cost of electricity for an efficient home in a particular neighborhood of Cincinnati, Ohio was $105 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: 105 Ha: > 105

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

b. What is the Type I error in this situation? The Type I error is H0 when it is accepting or rejecting? H0 when it is true or false? What are the consequences of making this error?

c. What is the Type II error in this situation? The Type II error is accepting or rejecting? H0 when it is true or false? What are the consequences of making this error?

Explanation / Answer

a. Our conclusion will be that the cost of electricity for a comparable neighborhood in Chicago, Illinois is higher than the same in Cincinnati, Ohio. (Ans).

b. Type I error is rejecting H0, when H0 is True. Here, the Type I error is concluding cost of electricity in Chicago is significantly higher than Cincinnati, when it is actually not. Type I error is more fatal and will result in misleading conclusion. (Ans).

c. Type-Ii error is fail to reject H0, when it is actually False. Here, the Type II error will occur if we conclude that cost of electricity in Chicago is not significantly higher than Cincinnati, when it is actually higher. Type-II error is comparatively less fatal than Type-I error, although it will also result in incorrect conclusion. (Ans).

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