The stability of measurements of the characteristics of a manufactured product is important in maintaining product quality. In fact, it is sometimes better to obtain small variation in the measured value of some important characteristic of a product and have the process mean slightly off target than to get wide variation with a mean value that perfectly fits requirements. The latter situation may produce a higher percentage of defective product than the former.
A manufacturer of light bulbs suspected that one of his production lines was producing bulbs with a high variation in length of life. To test this theory, he compared the lengths of life of n = 50 bulbs randomly sampled from the suspect line and n = 50 from a line that seemed to be in control. The sample means and variances for the two samples were as shown in the following table.
| Suspect Line |
Line in Control |
| y-1 = 1520 |
y-2 = 1476 |
| s12 = 92000 |
s22 = 37000 |
a. Do the data provide sufficient evidence to indicate that bulbs produced by the suspect line possess a larger variance in length of life than those produced by the line that is assumed to be in control? Use α = .05.
b. Find the approximate observed significance level for the test and interpret its value.