Statistics II ECN 2002

Statistics II                                                                                                                   

ECN 2002                                                                

Final Exam

Problems: Answer each question

1. A quality control expert is called in to determine whether a newly installed machine is meeting quality standards in producing a particular cotton cloth according to the specifications set by the manufacturer. The mean warp-breaking strength of this particular cotton cloth has been established to be 66 pounds. A random sample of 36 pieces of cotton cloth is obtained from a production run on this machine. The results of the sample reveal a mean warp-breaking strength of 64.5 pounds and a standard deviation of 5 pounds. Can the quality control expert make the decision that the cotton produced on the new machine meets the warp-breaking specification of the manufacturer at the .05 level of significance?

2.The personnel director of a large insurance company is interested in reducing the turnover rate of data processing clerks in the first year of employment. Past records indicate that 25% of all new hires in this area are no longer employed at the end of one year. Extensive new training approaches are implemented for a sample of 150 new data processing clerks. At the end of a one-year period, 29 of these 150 individuals are no longer employed. At the .01 level of significance, is there evidence that the proportion of data processing clerks who have gone through the new training and are no longer employed is less than .25? If not does personnel need to review and possibly revise its new training approach?  

3. In an effort to reduce departmental fuel costs for its fleet of government cars, senior level management at the Justice Department is trying to decide which major gasoline brand to direct field staff to use when on the road. In making that decision, management is trying to determine which gasoline brand offers the best performance for the price. An independent testing agency has been contracted to determine whether there is any difference in gasoline mileage output of two different gasolines used in the same model automobile. The first gasoline was tested on 200 cars and produced a sample average of 18.5 miles per gallon with a standard deviation of 4.6 miles per gallon. The second was tested on a sample of 100 cars and produced a sample average of 19.34 miles per gallon with a standard deviation of 5.2 miles per gallon. At the .05 level of significance, can a decision be made that there is evidence of a difference in performance of the two gasolines and can a choice be made?

4. The director of manufacturing of baseballs is investigating vendors who supply them regularly to ML baseball. The director would like to estimate the diameter of the baseballs that are currently used in the toy line to determine if they still comply with league specifications. The principal manufacturing vendor has specified that the baseballs are supposed to have a population mean diameter of 7.30 inches and a standard deviation equal to .04 inches. A random sample of 25 selected from a shipment indicates a sample average of 7.31 inches. Set up a 95% confidence interval estimate of the true average diameter of baseballs in this shipment. Does the director need to choose another manufacturer? Does the population of baseballs need to have a diameter that is normally distributed here?