Question: For the data in Exercise, the trimmed mean is X t = 42.17 with a Winsorized standard deviation of sw = 1.73. Test the hypothesis that the population trimmed mean is 45 with α = 0.05.
Exercise: A company claims that on average, when exposed to its toothpaste, 45% of all bacteria related to gingivitis is killed. You run 10 tests and find that the percentages of bacteria killed among these tests are 38, 44, 62, 72, 43, 40, 43, 42, 39, 41. The mean and standard deviation of these values are X¯ = 46.4 and s = 11.27. Assuming normality, test the hypothesis that the average percentage is 45 with α = 0.05.