1. A manufacturer of men's underwear claims that 93 percent of the products are of the "best" quality, 6 percent are "seconds", and only 1 percent are defective. To test this claim, 500 garments selected at random are inspected; the inspection results in the respective frequencies of 475, 18 and 7. (a) Write down your null hypothesis and alternative hypothesis to test the manufacturer's claim. Let 1 = best quality, 2 = seconds, and 3 = defective. (b) Determine the critical region for this test (where you would reject the null hypothesis) for = 0.05. (c) Perform a test to determine if the manufacturer's claim was valid or not. What conclusion do you reach (does the claim appear valid or not)?