A manufacturer of doorknobs has a production process that is designed to provide a doorknob with a target diameter of 2.5 inches. In the past, the standard deviation of the diameter has been 0.035 inch. In an effort to reduce the variation in the process, various studies have resulted in a redesigned process. A sample of 25 doorknobs produced under the new process indicates a sample standard deviation of 0.025 inch.
a. At the 0.05 level of significance, is there evidence that the population standard deviation is less than 0.035 inch in the new process?
b. What assumption do you need to make in order to perform this test?
c. Compute the p-value in (a) and interpret its meaning.