Due to the sharp rise in oil prices, the cost of heating a home rose sharply in the winter of 2008. The average cost was $1,044, which was an increase of 33% above that in 2007. In addition to concern over the increase in average heating costs was the possibility of a sharp increase in the variability in heating costs. This could signal that lower income families were simply not heating their homes as much, whereas those in higher income brackets were heating their homes as required.

The file entitled Homeheat contains a sample of heating costs that accrued during the winter of 2008.

Historical data indicate that heating costs have had a standard deviation of about $100.

a. Conduct a test of hypothesis to see if the variability in heating costs in the winter of 2008 was larger than that indicated by historical data. Use both the test statistic and a significance level of 0.025.

b. Construct a box and whisker plot and determine whether it indicates that the hypothesis test of part a is valid.