A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.25 centimeters. If the variance of the diameters is equal to 0.015, then the machine is working as expected. A random sample of 18 bolts has a standard deviation of 0.0175. Does the manufacturer have evidence at the α=0.005 level that the variance of the bolt diameters is less than required? Assume the population is normally distributed.

Step 1 of 5 : State the null and alternative hypotheses. Round to four decimal places when necessary.