Examples of Population Variance Determination

Five samples are taken from a normal population of parts from a factory with average = 3 and CT = 1. The samples are 2.0, 2.5, 3.0, 3.5, and 4.0. Does this sample of parts support the belief that the sample came from the factory with a equal to 1?

X of sample = 3 and s of the sample = 0.79. From Equation (5.8)

The calculated value of x2 (2.50) with v = 4 is close to 50% confidence (3.357) and is in between the 90% and 10% (1.064-7.779) confidences. Therefore, based on variance, it is highly likely that the sample was made at that factory.

Example 5.9

Nine samples (from Example 5.7) were taken from an assumed normal population with the following values from example: 5.7: 2.6, 2.1, 2.4, 2.5, 2.7, 2.2, 2.3, 2.4, and 1.9. What are the 95% and 99% confidence intervals of population variance?

Sample data: n = 9; average = 2.34, and s = 0.25.

Confidence

a = 0.05, therefore the 95% confidence limits are 0.025 and 0.975 @ v =：8:

8 * (0.25)2/17.535 < a2 < 8(0.25)2/2.180 0.0285 < o-2 < 0.229 or 0.17 <CT < 0.48 99% Confidence

a = 0.01, therefore the 99% confidence limits are 0.005 and 0.995 @ v =8:

8 • (0.25)2/21.955 < a2 < 8(0.25)2/1.344

0.0228 < a2 < 0.372 or 0.15 < a- < 0.61

Note that the confidence interval gets larger as the confidence limits increase.