A major car manufacturer wants to test a new engine to determine whether it meets new air-pollution standards. The mean emission u of all engines of this type must be less than 20 parts per million of carbon. Thirty five new engines were tested, and the emission level of each is determined. A mean and standard deviation of 19.7 and 1.18, respectively, are computed. (a) State the null and alternative hypothesis in a test to determine if the data provide sufficient evidence to conclude that this type of engine meets the pollution standard. (b) Find the value of the test statistic. (c) Find the observed significance level (P-value) of the test. (d) What would you conclude at the a = .05 level of significance ? (e) What would you conclude at the a = .1 level of significance ? (f) What is the probability of a type II error of the test procedure in (d) when the actual value of / = 19.5