Question

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 100 Duracell and

Y

be the sample average lifetime of 100 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?

The answer decreases as the sample size increases.

The answer increases as the sample size decreases.   

The answer decreases as the sample size decreases.

The answer is the same irrespective of the sample sizes.

The answer increases as the sample size increases.

(b)

Suppose the population standard deviations of lifetime are 1.8 hours for Duracell batteries and 3.0 hours for Eveready Energizer batteries. With the sample sizes given in part (a), what is the variance of the statistic

X − Y,

and what is its standard deviation? (Round your answers to four decimal places.)

variance=standard deviation=

Answer 1