Three different brands of car batteries, each having a 42 month warranty, were included in a study of battery lifetime. A random sample of batteries of each brand was selected, and lifetime, in months, was determined.

An analysis of variance was conducted and the p-value was 0.053. The hypothesis that all mean lifetimes are the same was retained at the 5% level.

Multiple comparisons of the means were also carried out with the following (somewhat contradictory) findings:

The Tukey's 95% simultaneous comparisons found no significant differences between the mean lifetime for the different brands.

Fisher's 95% individual confidence intervals, on the other hand, concluded that Brand 4 had the highest mean lifetime, but didn't differ significantly from Brands 2 and 3. And Brand 1 had the lowest mean lifetime, but it didn't differ significantly from Brand 2.

QUESTION: How could you explain what appears to be contradictory findings? From the options below, choose the statement that really doesn't help to explain the contradiction.

a. The Type1 error rate associated with Fishers simultaneous confidence intervals is greater than the Type 1 error rate associated with the test conducted in the ANOVA table. So contradictions are possible

b. The level of significance should be set at 10% so we can conclude that the mean lifetime for at least one Brand differs.

c. Tukey's 95% simultaneous confidence intervals are more conservative than Fisher's individual confidence intervals.

d. There is more than a 5% chance that at least one of Fisher's intervals has not captured the population difference it is estimating.

e. The Type 1 error rate associated with Tukey's simultaneous confidence intervals is the same (5%) as the level of significance that used in the ANOVA test so we expect consistent conclusions