Question

the u.s. energy information administration claimed that u.s. residential customers used an average of 10,176 kilowatt hours (kwh) of electricity this year. a local power company believes that residents in their area use more electricity on average than eia's reported average. to test their claim, the company chooses a random sample of 122 of their customers and calculates that these customers used an average of 10,559kwh of electricity last year. assuming that the population standard deviation is 2756kwh , is there sufficient evidence to support the power company's claim at the 0.05 level of significance?

Answer 1

To test the power company's claim, perform a hypothesis test using the sample data and a significance level of 0.05.

Step-by-step explanation:

To test the power company's claim, we will perform a hypothesis test using the sample data. The null hypothesis, denoted as H0, is that the average electricity usage of the power company's customers is the same as the average reported by the U.S. Energy Information Administration (EIA).

The alternative hypothesis, denoted as Ha, is that the power company's customers use more electricity on average than the EIA's reported average.

We will use a one-sample t-test since we have the sample mean, sample size, and the population standard deviation.

Using a significance level of 0.05, we will compare the calculated t-value with the critical t-value from the t-distribution table. If the calculated t-value is greater than the critical t-value, we will reject the null hypothesis and conclude that there is sufficient evidence to support the power company's claim.