Essential Statistics

Chapter 11: Confidence Intervals – Large Samples

499

11-5 Large Sample Confidence Interval for the Difference

Between Two Population Means

In this section, we will consider estimating the difference between two

population means.

Figure 11-18

shows the design of the situation at hand.

We will be sampling from two populations with unknown means. We will let

these population means respectively be denoted by

and

. We will

assume that the standard deviations for the respective populations are

and

. We will also assume that these standard deviations are known and that

the populations are normally distributed. In addition, if the normality

assumption cannot be made, the sample sizes will be assumed to be large

enough such that the

Central Limit Theorem

for the difference between the

sample means will hold. Samples of size

and

will be obtained and the

sample means will be computed.

Figure 11-18:

Display of the experimental situation in

selecting samples to estimate the

difference between two population means

The point estimate for the population means can be computed from

∑

and

∑

and we will consider

as the point estimate for

, the difference between the two population means. That is,