1. In recent years , the policy of lead production in the United States has been to produce at total capacity rate but with no overtime permitted. Thus the production in any month should be independent of production in the following month . A U.S. Senator has expressed concern over a suspected increase in the national production of lead , but the monthly production figures over the past few years have shown large variation. Before a large-scale investigation of production is launched, the monthly figures shown in the Table below will be studied for patterns in the fluctuations. Test for HD : Monthly production is a random process versus H1 : Monthly production gures exhibit a pattern of clustering Table 1; Mine Production (in thousands of short tons) Month 1969 1970 1971 Jan . 37.2 47.8 45.3 Feb. 35.1 46.9 41.9 Mar . 39.3 52.5 52.7 Apr . 42.6 49.7 47.1 May 44.2 51.3 45.6 June 45.5 47.4 45.4 July 44.4 46.6 Aug . 45.4 48.1 Sept . 43.5 48.6 Oct . 41.7 46.5 Nov. 41.5 48.5 Dec . 41.4 45.3 2. (Contingency Table) Suppose that 20 out of 50 females and 10 out of 40 males are depressed in a sample . Determine whether the frequency of depression is related to sex. 3. We are interested in investigating the proportions of four blood types (ABO system). Somehow we believe that 34% of people have blood type A, 15% blood type B, 23% blood type AB, and 28% blood type 0. We go out to campus and collect a sample of 100 students, and find the following: A: 12, B: 56, AB: 2, O: 30. What do you conclude? State the null hypothesis and compute the pvalue