The Bonferroni theorem states that the probability that at least one of a set of events occurs can be no greater than the sum of the separate probabilities of the events. For instance, if the probability of an error for each of five separate confidence intervals equals 0.01, then the probability that at least one confidence interval will be in error is no greater than (0.01 + 0.01 + 0.01 + 0.01 + 0.01) = 0.05.
a. Following Example 10, construct a confidence interval for each factor and guarantee that they both hold with overall confidence level at least 95%. [Each interval should use t.0125 = 2.46.]
b. Exercise 14.8 referred to a study comparing three groups (smoking status never, former, or current) on various personality scales. The study measured 35 personality scales and reported an F test comparing the three smoking groups for each scale. The researchers mentioned doing a Bonferroni correction for the 35 F tests. If the nominal overall probability of Type I error was 0.05 for the 35 tests, how small did the P-value have to be for a particular test to be significant? (What should the Type I error probability be for each of 35 tests in order for the overall Type I error probability to be no more than 0.05?)