7. Precision valves for controlling the flow of fluids and liquids can be assembled in a clean room or on a less-clean production line. The cleanliness of the assembly process can affect the leak rate. Twenty valve assemblies were made on the production line and another twenty were made in the clean room. The same component lots were used for all forty assemblies. a. There were three leakers from the production line versus zero leakers from the clean room. Is there sufficient evidence to conclude that the leak rate on the production line is worse than the leak rate in the clean room? b. What's the smallest number of defectives that would have to be found on the production line with no defectives found in the clean room to conclude that the production line leaker rate is worse that in the clean room?

8. An application of the distribution of sample means People suffering from hypertension, heart disease, or kidney problems may need to limit their intakes of sodium. The public health departments in some US states and Canadian provinces require community water systems to notify their customers if the sodium concentration in the drinking water exceeds a designated limit. In Massachusetts, for example, the notification level is 20 mg/L (milligrams per liter). Suppose that over the course of a particular year the mean concentration of sodium in the drinking water of a water system in Massachusetts is 18.6 mg/L, and the standard deviation is 6 mg/L. Imagine that the water department selects a simple random sample of 31 water specimens over the course of this year. Each specimen is sent to a lab for testing, and at the end of the year the water department computes the mean concentration across the 31 specimens. If the mean exceeds 20 mg/L, the water department notifies the public and…

4. Suppose that we want to compare the cholestrol contents of four competing diet foods on the basis of the following data (in milligrams per package) which were obtained for three 6-ounce packages of each of the diet foods: Diet food A: 3.6 4.1 4.0 Diet food B: 3.1 3.2 3.9 Diet food C: 3.2 3.5 3.5 Diet food D: 3.5 3.8 3.8 a) Fill in the blanks below. b) Test at the 0.05 level of significance whether the differences among means obtained for the four competing diet foods (Diet A, B, C, D) are significant? Etable=4.07) ONE-WAY ANOVA TABLE Source of Degrees of Sum of Squares Mean Square F Variation Freedom Treatments ? 0.54 ? ? Error ? ? ? Total ? 1.18

Based on Angel et al. (2003). A fertilizer companyis trying to determine the cheapest fertilizer mix thatprovides desired amounts of nutrients. The mix ismade by combining the following fertilizers: SSA,SPO, GUR, TSP, KCI, FERT, and SPF. The mix cannot contain both GUR and TSP. The percentage ofpotassium (K), sulfur (S), calcium (Ca), sodium (Na)and phosphorus (P) in each fertilizer is listed in the fileP06_88.xlsx. For example, a pound of SSA is 16% Kand 26% Na. The mix must contain at least 600 poundsof K, 550 pounds of S, 750 pounds of Ca, 900 poundsof Na, and 750 pounds of P. The mix cannot containboth GUR and TSP, because if both are present in themix, the affect of other fertilizers is nullified. The costper pound (in cents) of each fertilizer is listed in thesame file. Develop a linear integer model to find theminimum-cost fertilizer mixture that meets the statedchemical requirements.