This question has 4 parts. A chemical plant can dispose a certain amount of wastewater into a river. The Environmental Protection Agency (EPA) takes samples of the river water at several locations downstream from the plant. If the plant complies with the EPA regulations, the population mean number of toxic particles in the water is p. = 50 parts per million (ppm). Each day, the EPA selects 36 water samples and computes the average number of toxic particles, and then uses this information to determine if they should conclude that the population mean number of toxic particles is greater than 50 ppm. If so, the owner of the plant will be ned. Use the hypotheses H0 : ,u, g 50 ppm and HG : pi > 50 ppm. It is Known that the population standard deviation, 0, is 8 ppm of toxic particles. i) What is the most suitable test distribution for the one-sample test statistic? O The standard Normal distribution, N (0, 1) O The Student's t-distribution on 8 degrees of freedom 0 The Student's t-distribution on 36 degrees of freedom The Normal distribution N(52.3,82) O The Student's t-distribution on 35 degrees of freedom ii) Determine the test statistic for this test with a sample mean of :E : 52.3 ppm 0 z = 2.23 O t = 1.725 O z = 1.725 O t = 2.23 O t = 1.725 iii) If the EPA use a 5% significance level, give the appropriate conclusion for this test with a sample mean of x = 52.3 ppm O The test statistic falls into the rejection region, so the number of toxic particles exceeds 50 ppm on average and the owner must pay a fine O The test statistic falls into the rejection region, so there is 5% probability that the distribution we had chosen was wrong and the owner does not pay a fine O The test statistic does not fall into the rejection region, so the number of toxic particles exceeds 50 ppm on average and the owner must pay a fine O The test statistic falls into the rejection region, so the number of toxic particles exceeds 50 ppm on average in only 5% of the samples taken and the owner must pay a fine O The test statistic does not fall into the rejection region, so we cannot conclude anything, and the owner does not pay a fineiv) Due to a change in the personnel responsible for monitoring the quality of the plant's wastewater, the population mean number of toxic particles in the water during a given month is p, = 54.1 ppm. The population standard deviation remained the same with cur : 8 ppm. What is the probability that on a given day this month, the average amount of toxic particles determined from 36 water samples will not result in the owner of the plant being ned? [Hint: Consider the possibility of a Type II error] 0 0.92 O 0.10 O 0.05 O 0.08 O 0.95