APPENDIX D 811 9. x = 5.6955 g, R = 0.2054 g. For R chart: LCL = 0.0000 g and UCL = 0.4342 g. For x chart: LCL = 5.5770 g and UCL = 5.8140 g. 11. There are points lying beyond the upper control limit, so the process mean appears to be out of statistical control. 13. Except for a different vertical scale, the s chart is nearly identical to the R chart shown in Example 3. Section 14-2 1. No, the process appears to be out of statistical control. There is a downward trend and there are at least eight consecutive points all lying above the centerline. Because the proportions of defects are decreasing, the manufacturing process is not deteriorating; it is improving. 3. Because the value of -0.00325 is negative and the actual proportion of defects cannot be less than 0, we should replace that value with 0. 5. The process appears to be within statistical control. (Considering a shift up, note that the first and last points are about the same.) 5. Test statistic: T = 27. Critical value: T = 8. Fail to reject the null hypothesis that the population has a median of 4.5333 g. 6. 4.4722 g 6 m 6 4.6426 g. Because the confidence interval contains the claimed mean of 4.5333 g, there is not sufficient evidence to warrant rejection of the claim that the population mean is equal to 4.5333 g. 7. Answers vary, but here is a typical answer: 4.4924 g 6 m 6 4.6293 g. Because the confidence interval contains the claimed mean of 4.5333 g, there is not sufficient evidence to warrant rejection of the claim that the population mean is equal to 4.5333 g. 8. The sample mean is 55.15 years. n1 = 22, n2 = 17, and the number of runs is G = 17. mG = 20.17949, sG = 3.029127. Test statistic: z = -1.05. Tech: P@value = 0.2939. Critical values: z = {1.96. Fail to reject the null hypothesis of randomness. There is not sufficient evidence to warrant rejection of the claim that the sequence of ages is random relative to values above and below the mean. The results do not suggest that there is an upward trend or a downward trend. 9. 2401 10. There must be an error, because the rates of 13.7% and 10.6% are not possible with samples of size 100. Chapter 14 Answers Section 14-1 1. a. A run chart is a sequential plot of individual data values over time. It is used to monitor process data for any patterns of changes over time. b. An R chart is a plot of sample ranges. It is used to monitor the variation in a process. c. An x chart is a plot of sample means. It is used to monitor the center in a process. 3. A process is statistically stable (or within statistical control) if it has only natural variation, with no patterns, cycles, or significantly low or significantly high points. 5. x = 267.11 lb, R = 54.96 lb. For R chart: LCL = 4.18 lb and UCL = 105.74 lb. For x chart: LCL = 244.08 lb and UCL = 290.14 lb. 7. The R chart does not meet any of the three out-of-control criteria, so the variation of the process appears to be within statistical control.
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