Highway engineers have found that many factors affect the performance of reflective highway signs. One is the proper alignment of the automobile’s headlights. It is though that more than 50 % of the automobiles on the road have misaimed headlights. If this contention can be supported statistically, then a new tougher inspection program will be put into operation. Let p denote the proportion of automobiles in operation that have misaimed headlights. Since we wish to support the statement that p > .5, this contention is taken as the alternative or research hypothesis, H1. The null hypothesis is the negation of H1.1. State the hypotheses.2. What are the possible end results for any test of a hypothesis?3. A random sample of 20 cars is selected and the headlights are tested. Design a test so that alpha, the probability of rejecting H0 when p is equal to the null value of .5, is about .05.4. Suppose we define the critical region for the above problem as C = {14, 15, 16…20}, and that, unknown to the researcher, the true proportion of cars with misaimed headlights is .7. What is the probability that our test is unable to detect this situation? What if the true proportion is .8?5. The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard.6. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard.7. Discuss the practical consequences of making a Type I and a Type II error.