The Environmental Protection Agency (EPA} sets a limit of 5 parts per million on PCB (a dangerous substance) in water. A manufacturing rm, which produces PCB for electrical insulation, discharges small amounts from its plant. The company's management, in an effort to avoid water pollution, has given instructions that production may continue only if there is convincing evidence that the mean amount of PCB in the plant's efuent is less than 5 parts per million. A random sample of fty water specimens is taken, and the sample mean amount of PCB is calculated. Based on the results of the sample, the plant will decide whether to continue production. A. Give the appropriate null and alternative hypotheses for the stated experimental objective. B. Dene a Type I error and a Type II error in this context. C. Discuss the consequences of the errors in Part B. D. Considering your answers above, what value of a would you select for the test? E. Suppose the sample of 50 water specimens yields a mean of 4.78 parts per million of PCB. Complete the appropriate test of hypothesis using the value of a you selected in Part D. The value of s is known to be 0.52 parts per million