The stability of measurements on a manufactured product is important in maintaining product quality. In fact, it is sometimes better to have small variation in the measured value of some important characteristic of a product and have the process mean be slightly off target than to suffer wide variation with a mean value that perfectly fits requirements. The latter situation may produce a higher percentage of defective products than the former. A manufacturer of light bulbs suspected that one of her production lines was producing bulbs with a wide variation in length of life. To test this theory, she compared the lengths of life for 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 follows:

“Suspect Line”         Line “in Control”
x̅1 = 1520................................x̅2 = 1476
s²₁ = 92,000........................s²₂ = 37,000

a. Do the data provide sufficient evidence to indicate that bulbs produced by the “suspect line” have a larger variance in length of life than those produced by the line that is assumed to be in control? Test using α = .05.

b. Find the approximate p-value for the test and interpret its value.