An article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes. (a) Let X be the sample average lifetime of 81 Duracell and Y be the sample average lifetime of 81 Eveready Energizer batteries.

What is the mean value of X − Y (i.e., where is the distribution of X − Y centered)?
Does your answer depend on the specified sample sizes?

A. The answer increases as the sample size decreases.
B. The answer is the same irrespective of the sample sizes.
C. The answer decreases as the sample size increases.
D. The answer decreases as the sample size decreases.
E. The answer increases as the sample size increases.

Given that an article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively

Let X be the sample average lifetime of 81 Duracell and Y be the sample average lifetime of 81 Eveready Energizer batteries.

Now we have sample mean difference does not depend about the sample sizes.

This is because

E(X-Y) = E(X)-E(Y) for all X and Y

Mean of X-Y = [tex]4.1-4.5=-0.4[/tex]

This does not depend on the specified sample sizes

B. The answer is the same irrespective of the sample sizes.