Data Analysis with Microsoft Excel: Updated for Office 2007

206 Fundamentals of Statistics

size, xand s will estimate the true values of m and s to whatever degree of

precision is required. Figure 5-19 shows how the value of xapproaches the

value of m as the sample size increases.

Figure 5-19

Sample

averages

as the

sample size

increases

the sample average approaches

the value of m as the number

of observations in the

sample increases

The key question is How large must the sample be to estimate accurately

the value of m? To answer this question, we have to examine the properties

of the sample average.

The Sampling Distribution

Because the sample average is calculated by taking the average of random

variables, it is also a random variable following its own probability distribu-

tion called the sampling distribution. If we know the form of the sampling

distribution. we can make inferences about the sample average.

We’ll start our exploration of the sample average by creating nine random

samples of standard normal data, each sample containing 100 observations.