Question

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.

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.	There is more than a 5% chance that at least one of Fisher's intervals has not captured the population difference it is estimating.
	b.	Tukey's 95% simultaneous confidence intervals are more conservative than Fisher's individual confidence intervals.
	c.	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
	d.	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
	e.	The level of significance should be set at 10% so we can conclude that the mean lifetime for at least one Brand differs.

Answer 1

Using Tukey's method, you specify that the entire set of confidence intervals should have a 95% simultaneous confidence level. Minitab calculates that the 10 individual confidence levels need to be 99.35% to obtain the 95% simultaneous confidence level. These wider Tukey confidence intervals provide less precise estimates of the population parameters but limit the probability that one or more of the confidence intervals does not contain the true difference to a maximum of 5%.

Confidence intervals with 95% individual confidence levels

b)

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