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EQC7016 Statistical Methods for Quality Management Week 2 Exercises Sem 1 2020/2021 Statistical Quality Control – A Modern Introduction (7th Ed), International Edition; Douglas Montgomery Chapter 3 3.3. The content of liquid detergent bottles is being analyzed. Twelve bottles, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07 a) Calculate the sample average. b) Calculate the sample standard deviation 3.4. The service time in minutes from admit to discharge for ten patients seeking care in a hospital emergency department are 21, 136, 185, 156, 3, 16, 48, 28, 100, and 12. Calculate the mean and standard deviation of the service time. 3.5. The Really Cool Clothing Company sells its products through a telephone ordering process. Since business is good, the company is interested in studying the way that sales agents interact with their customers. Calls are randomly selected and recorded, then reviewed with the sales agent to identify ways that better service could possibly be provided or that the customer could be directed to other items similar to those they plan to purchase that they might also find attractive. Call handling time (length) in minutes for 20 randomly selected customer calls handled by the same sales agent are as follows: 5, 26, 8, 2, 5, 3, 11, 14, 4, 5, 2, 17, 9, 8, 9, 5, 3, 28, 22, and 4. Calculate the mean and standard deviation of call handling time. Chapter 4 4.7. The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of 0.002 cm. A random sample of 15 bearings has an average inside diameter of 8.2535 cm. (a) Test the hypothesis that the mean inside bearing diameter is 8.25 cm. Use a two sided alternative and α = 0.05 (b) Find the P-value for this test. (c) Construct a 95% two-sided confidence interval on the mean bearing diameter. 4.10. Using the data from Exercise 4.7, construct a 95% lower confidence interval on mean battery life. Why would the manufacturer be interested in a onesided confidence interval? 4.8. The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens is selected, and the average tensile strength is found to be 127 psi. (a) Test the hypothesis that the mean tensile strength equals 125 psi versus the alternative that the mean exceeds 125 psi. Use α = 0.05. (b) What is the P-value for this test? (c) Discuss why a one-sided alternative was chosen in part (a). (d) Construct a 95% lower confidence interval on the mean tensile strength. 4.9. The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the following lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. (a) The manufacturer wants to be certain that the mean battery life exceeds 25 h. What conclusions can be draw (b) Construct a 90% two-sided confidence interval on mean life in the accelerated test. 4.12. A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.06, 11.98, 11.97, 12.02, 12.05, and 11.99. (a) Suppose that the manufacturer wants to be sure that the mean net contents exceeds 12 oz. What conclusions can be drawn from the data (use α = 0.01). (b) Construct a 99% two-sided confidence interval on the mean fill volume. 4.16. Two machines are used for filling glass bottles with a soft-drink beverage. The filling have known standard deviation of 1 = 0.010 liter and 2= 0.005 liter processes respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 15 bottles from machine 2 results in average net contents of 1 x = 2.03 liters and 2 x = 2.07 liters. (a) Test the hypothesis that both machines fill to the same net contents, using α = 0.05. What are your conclusions? (b) Find the P-value for this test. (c) Construct a 95% confidence interval on the difference in mean fill volume. 4.17. Two quality control technicians measured the surface finish of a metal part, obtaining the data in Table 4E.1(Refer to Data File) Assume that the measurements are normally distributed. a) Test the hypothesis that the mean surface finish measurements made by the two technicians are equal. Use α = 0.05 and assume equal variances. b) What are the practical implications of the test in part (a)? Discuss what practical conclusions you would draw if the null hypothesis were rejected. c) Assuming that the variances are equal, construct a 95% confidence interval on the mean difference in surface-finish measurements. d) Test the hypothesis that the variances of the measurements made by the two technicians are equal. What are the practical implications if the null hypothesis is rejected?