The stability of measurements of the characteristics of a manufactured product is

Chapter 10, Problem 10.122

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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 y1 = 1,520 y2 = 1,476 s2 1 = 92,000 s2 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 = .05. b Find the approximate observed significance level for the test and interpret its value.