(a). (6 points) For the population of all homeowners who rake/bag their leaves, it is coniectured that the mean number of bags of leaves produced is 24, and of interest is to test this conjecture versus the alternative that the mean number of bags of leaves produced is different from 24 bags. State the appropriate null and alternative hypotheses that should be tested. (b). (20 points)Consider the information and hypotheses specified in part (a).A simple random sample of 51 homeowners was selected and the number of bags of leaves produced was recorded for each. The mean number of bags produced for this sample of 51 homeowners was 26.3 bags, with a standard deviation of 7.5 bags. If appropriate, use this information to test the hypotheses stated in part (a) at the a = .10 level of significance