The stability of measurements of the characteristics of a
Chapter 10, Problem 122SE(choose chapter or problem)
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 bulbs randomly sampled from the suspect line and
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 |
\(\overline{y_{i}}=1,520]) |
\(\overline{y_{2}}=1,476\) |
\(s_{1}^{2}=92,000\) |
\(s_{2}^{2}=37,000\) |
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 .
b Find the approximate observed significance level for the test and interpret its value.
Equation transcription:
Text transcription:
\overline{y{i}}=1,520
\overline{y{2}}=1,476
s{1}^{2}=92,000
s{2}^{2}=37,000
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