Metal works, a supplier of machine parts, fabricates bearings for use in aeronautical applications in which the standard deviation of the bearing diameter must be within 0.002 inch maximum. Otherwise, problems with fit will occur. The engineering department is conducting an experiment to investigate adherence to this requirement.
A sample of 25 bearings has revealed a sample standard deviation of 0.0024 inch.
a. State the appropriate null and alternative hypotheses to test if the requirement has been violated.
b. Compute the value of the test statistic. What assumption did you make regarding the bearing diameters?
c. Use the p-value approach to conduct the test at α = 0.05. What is your conclusion?
d. Would your conclusion change at the 10% significance level?