Introductory Biostatistics

mal curve. This resemblance is much clearer with real populations and

larger sample sizes.

We now consider the same population and all possible samples of sizen¼4.
Table 4.3 represents the new sampling distribution. It can be seen that we have
a di¤erent sampling distribution because the sample size is di¤erent. However,
we still have both above-mentioned properties:

1. Unbiasedness of the sample mean:

ð 3 Þð 0 : 25 Þþð 9 Þð 0 : 50 Þþð 3 Þð 0 : 75 Þ

15

¼ 0 : 5

2. Normal shape of the sampling distribution (bar graph; Figure 4.2).


3. In addition, we can see that the variance of the new distribution is
   smaller. The two faraway values ofx, 0 and 1, are no longer possible;
   new values—0.25 and 0.75—are closer to the mean 0.5, and the majority
   (nine samples) have values that are right at the sampling distribution
   mean. The major reason for this is that the new sampling distribution is
   associated with a larger sample size,n¼4, compared ton¼3 for the
   previous sampling distribution.

TABLE 4.3

Samples

Number of

Samples

Value of

Sample Mean,x

(A, D, E, F), (B, D, E, F), (C, D, E, F) 3 0.25

(A, B, D, E), (A, B, D, F), (A, B, E, F)
(A, C, D, E), (A, C, D, F), (A, C, E, F)
(B, C, D, E), (B, C, D, F), (B, C, E, F) 9 0.50

(A, B, C, D), (A, B, C, E), (A, B, C, F) 3 0.75

Total 15

Figure 4.2 Normal shape of sampling distribution for Example 4.1.

BASIC CONCEPTS 151