Question

Suppose a researcher wants to compare two formulations of moisturizing sun block. The 20 participants tried both formulations, one formulation on each side of their backs. Ten participants were randomly assigned to receive formulation A on the right side of the back and formulation B on the left side. The other 10 participants received formulation A on the left side of the back and formulation B on the right side. The researcher obtained skin dryness scores for each participant for each formulation.

The researcher establishes the hypothesis for the test.

Ho: There is no difference in the population distributions of skin dryness scores for the two formulations of sunscreen.
H1: One population's distribution of skin dryness scores is sytematically higher or lower than the other's.

The value of W+, the sum of the positive ranks, is 161.5.

What is the z‑statistic for this test using the normal approximation? You do not need to use a continuity correction and can use this z‑table. Round your answer to two decimal places.

z=

What is the P-value for this test? Round your answer to three decimal places.

P-value=

Answer 1

nA = 10, nB = 10, Sum of ranks W = 161.5

= nA(nA + nB + 1) / 2 = 10 * (21) / 2 = 105

= SQRT[nAnB * (nA + nB + 1) / 12] = SQRT[100 * 21 / 12] = 13.229

Therefore Z = (161.5 - 105) / 13.229 = 4.27

The P value (Right tail) = 0.000