Boeing has developed a new drilling tool that drills hole for riveting on the 787 wings. The standard deviation of hole diameter should be small enough to ensure that the rivet will fit. Boeing engineers took random samples of 16 from an old tool and 21 from a new tool. The two sample standard deviation of hole diameters were sold = 0.008 millimeters and snew= 0.01 millimeters. Is there strong evidence to indicate that the standard deviations of hole diameter drilled by the new drilling tool is smaller as compared to the old tool? Use alpha= 0.05.

a) Please state the appropriate null and alternative hypothesis.

b) Calculate appropriate statistics

c) Define the critical region