EXAMPLE 8.10

Sample size for comparing two sunblock lotions. In Example 8.5 (page 491), we performed the significance test for comparing two sunblock lotions in a setting where each subject used the two lotions and the product that provided better protection was recorded. Although your product performed better 13 times in 20 trials, the value of was not sufficiently far from the null hypothesized value of p₀ = 0.5 for us to reject the H₀, (p = 0.18). Let’s suppose that the true percent of the time that your lotion would perform better is p₀ = 0.65, and we plan to test the null hypothesis H₀: p = 0.5 versus the two-sided alternative H_a: p ≠ 0.5 using a Type I error probability of 0.05.

What sample size n should we choose if we want to have an 80% chance of rejecting H₀? Outputs from JMP and Minitab are given in Figure 8.4. JMP indicates that n = 89 should be used, while Minitab suggests n = 85. The difference is due to the different methods that can be used for these calculations.