Example 1 describes Allison’s experiment to determine whether a tanning lotion or a tanning studio produced a better tan. Table 15.1 showed the possible rankings for five tans. Table 15.2 showed the sampling distribution of the difference between the sample mean ranks, presuming the null hypothesis is true that the tanning treatments have identical effects. For Allison’s actual experiment, the ranks were (2, 4, 5) for the three participants using the tanning lotion and (1, 3) for the two participants using the tanning studio.

Questions to Explore

a. Find and interpret the P-value for comparing the treatments, using the one-sided alternative hypothesis that the tanning studio gives a better tan than the tanning lotion.

b. What’s the smallest possible P-value you could get for this experiment?