Due to the sharp rise in oil prices, the cost of heating a home has risen sharply. In a recent year, the average cost was $1,044, which was an increase of 33% above that in the previous year. 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 titled Homeheat contains a sample of heating costs that accrued. 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 sample 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.