According to the National Funeral Directors Association, the nation's 22,000 funeral homes collected an average $5,020 per full-service funeral in 1998, up from $4,780 in 1996 (Wall Street Journal Interactive Edition, Jan. 7,2000). In early 2000, a random sample of 36 funeral homes reported revenue data for 1999.

Among other measures, each reported its average fee for a full-service funeral during 1999. These data (in thousands of dollars) are shown in the table below, rounded to the nearest hundred. 6.1 8.1 4.0 7.1 6.2 5.2 4.9 7.0 5.4 10.3 5.0 4.6 5.4 4.5 3.9 5.1 4.7 6.1 5.9 5.3 5.0 4.0 5.3 4.3 7.1 5.9 6.1 4.5 5.0 4.8 5.7 5.9 4.8 4.1 6.1 5.3

a. What are the appropriate null and alternative hypotheses to test whethcr the average full-service fee of U. S. funeral homes in 1999 exceeds $5,020?

b. Conduct the test at n = .05 using a statistical software package. Do the sample data provide sufficient evidence to conclude that the average fee in 1999 was higher than in 1998?

c. In conducting the test, was it necessary to assume that population of average full-service fees was normally distributed? Justify your answer.