the u.s. energy information administration claimed that u.s. residential customers used an average of 10,400 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 163 of their customers and calculates that these customers used an average of 10,782kwh of electricity last year. assuming that the population standard deviation is 2768kwh, is there sufficient evidence to support the power company’s claim at the 0.01 level of significance?
-
There is not sufficient evidence to support the power company’s claim.According to the information given in the question, we can frame the hypothesis as follows-Null hypothesis ⇒ : H = 10400Alternate hypothesis ⇒ Ha: > 10400This is the right-tailed test.Test statistic = z[(x – μ)√n]/ σwhere x ⇒ sample mean = 10,782σ ⇒ standard deviation = 2768= (10782 – 10400)√163/ (2768)= 382* 12.76/(2768)= 1.76⇒ Test statistic z = 1.76Now, P( z > 1.76) = 1 – P( z < 1.76)= 1 – 0.9608= 0.0392using z tables-p-value = 0.0392a = 0.01we see that p-value > aThus, we fail to reject our null hypothesis.Therefore, there is not sufficient evidence to support the power company’s claim.Learn more about hypothesis testing here-https://brainly.com/question/29576929#SPJ4