Introductory Biostatistics

value ‘‘1,’’ the remaining, ‘‘0.’’ Table 4.2 represents the sampling distribution of
the sample mean.
This sampling distribution gives us a few interesting properties:

1. Its mean (i.e., the mean ofall possiblesample means) is

ð 1 Þð 0 Þþð 9 Þ^13



þð 9 Þ^23



þð 1 Þð 1 Þ

20

¼ 0 : 5

which is the same as the mean of the original distribution. Because of

this, we say that the sample mean (sample proportion) is anunbiased

estimatorfor the population mean (population proportion). In other

words, if we use the sample mean (sample proportion) to estimate the

population mean (population proportion), we arecorrect on the average.

2. If we form a bar graph for this sampling distribution (Figure 4.1). It
   shows a shape somewhat similar to that of a symmetric, bell-shaped nor-

TABLE 4.2

Samples

Number of

Samples

Value of

Sample Mean,x

(D, E, F) 1 0

(A, D, E), (A, D, F), (A, E, F)
(B, D, E), (B, D, F), (B, E, F)

(C, D, E), (C, D, F), (C, E, F) (^913)
(A, B, D), (A, B, E), (A, B, F)
(A, C, D), (A, C, E), (A, C, F)
(B, C, D), (B, C, E), (B, C, F) (^923)
(A, B, C) 1 1
Total 20
Figure 4.1 Bar graph for sampling distribution in Example 4.1.
150 ESTIMATION OF PARAMETERS