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 US. Senator has expressed concern over a suspected increase in the national production of lead, but the monthly production gures over the past few years have shown large variation. Before a large-scale investigation of production is launched, the monthly gures shown in the Table below will be studied for patterns in the uctuations. Test for H0 : Monthly production is a random process versus the alternative: 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 (Remark: In this question, the \"Runs Up and Downs\" method is recommended. If you like to compare with the ordinary runs test, that's good.)