10.116 Connector Rods A producer of machine parts claimed that the diameters of the connector rods produced by its plant had a variance of at most 0.173 cm. A random sample of 15 connector rods from the plant produced a sample mean and variance of 1.4 cm and 0.58 cm, respectively.

a. Is there sufficient evidence to reject the producer's claim at the a=0.05 level of significance?

b. Find a 95% confidence interval for the variance of the rod diameters.