(P2) (12 points) An experiment is run to study the effects of PCB, an industrial contaminant, on the reproductive ability of owls. The shell thickness (mm) of eggs produced by 10 owls exposed to PCB are compared to the shell thickness of eggs produced by 10 owls which did not have PCB exposures. Owl 1 2 3 4 5 6 7 8 9 10 PCB-Exposed: 3.6 3.2 3.8 3.6 4.1 3.8 4.2 3.4 3.7 3.8 UnExposed: 4.3 4.4 3.6 3.5 4.4 3.5 3.4 3.6 4.1 4.3 (A) Is there significant(o = .05) evidence that the PCB exposed owls have thinner egg shells than those of the unexposed owls? Use a t-test in reaching your conclusion and report the p-value. (B) Compute the chance that your test committed a Type II error for the following values of 0 = Herposed - Hunexposed = 0, -.50, -0, -1.50, -20. (C) In designing a new study, the researchers want to determine the necessary sample sizes for exposed and unexposed owls such that an o = .05 test will have power of at least 80% to detect a shell thickness difference of more than 0.3 mm. The researchers want to examine three times as many exposed owls as unexposed owls, that is, m=3n. (D) Is there significant(a = .05) evidence that the PCB exposed owls have thinner egg shells than those of the unexposed owls? Use a Wilcoxon test in reaching your conclusion and report the p-value. (E) Is there significant(a = .05) evidence that the PCB exposed owls have greater variability in egg shell thickness than those of the unexposed owls? Report the p-value of your test. (F) Which test, t-test or Wilcoxon, is more appropriate for testing the difference in egg shell thickness