# 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.