Problem 1 (25 points) Two additives to Portland cement are being tested for their effect on the strength of concrete. 21 batches were made with Additive A, and their strengths showed standard deviation SA = 41.3. 16 batches were made with the same percentage of Additive B, and their strengths showed standard deviation SB = 26.2. Assume that the strengths of concrete follow a normal distribution. (a) Is there evidence at the 1% level of significance that the concrete made with Additive A is more variable than concrete made with Additive B ? (b) Is there evidence at the 10% level of significance that concrete made with Additive A and concrete made with Additive B have different variabilities? (c) Illustrate the critical values, critical regions, and test statistics in part (a) and part (b)