A researcher new to the Tucson area was shocked when she received her first summ

Question

A researcher new to the Tucson area was shocked when she received her first summer electric bill. She believes that energy bills vary dramatically depending on where you live in the United States and sets out to test her claim. She samples 36 people from the Northeast, 100 people from the Southeast, 81 people from the Mid-West, and 200 people from the West. She finds the following average annual energy bills from each region: Northeast: $1,159.26 Southeast: $1,202.51 Mid-West: $1,300.04 West: $1,199.99 An ANOVA test in Excel which returns a p-value of.0005 with an MSE 94.12. She rejects the null hypothesis and concludes that there is some difference in the average annual electric bill based on the region. She is most interested in if there are differences between the Mid-West and the Southeast. She calculates a 95% Fisher's Confidence Interval and finds that the interval is between and $100.39. Let the Mid-West be i and the Southeast be j in the formula

Explanation / Answer

midwest -   1300.04

souteast = 1202.51

difference = 1300.04 - 1202.51 = 97.53

hence

(L +U)/2 = 97.53    {L- lower , U -upper

here U = 100.39

hence

L = 2 * 97.53 - 100.39 = 94.67

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