4. A manufacturing company claims that the defective rate for their product is 1%. The local government requires a monthly test to check the validity of this claim, and the company would have to pay a $100,000 penalty if it is found that the defective rate is above 1%. They set up two hypotheses: H0 : p = .01 H1 : p > .01 where p is the defective rate for the product. They select 5% significance level, and base their answer on the test statistics zstat = p .01 q .01(1.01) n . (a) What is the smallest sample size for making this test reliable? (b) What is the probability that the company will be unjustly penalized if the defective rate is 1%?