5.20 A manufacturer of suntan lotion is testing a new formula to see whether it provides more protection against sunburn than the old formula. The manufacturer chose 10 persons at random from among the company’s employees, applied the two types of lotion to their backs, one type on each side, and exposed their backs to a controlled but intense amount of sun. Degree of sunburn was measured for each side of each subject, with the results shown below (higher numbers represent more severe sunburn).

(a) Test the null hypothesis that the difference (old–new) of degree of sunburn has median zero against the one-sided alternative that it is negative, assuming that the differences are symmetric. Does the new formula appear to be effective?

(b) Find a two-sided confidence interval for the median difference, assuming symmetry and with confidence coefficient near 0.90.

(c) Do

(a) and

(b) without assuming symmetry.

Subject Old Formula New Formula 1 41 37 2 42 39 3 48 31 4 38 39 5 38 34 6 45 47 7 21 19 8 28 30 9 29 25 10 14 8