Applied Statistics and Probability for Engineers

Analysis of a Second-Order Response Surface When the experimenter is relatively close to the optimum, a second-order model is us ...

Table S14-9 summarizes the analysis of variance for this model. The response surface is shown graphically in Fig. S14-12. Notice ...

14-18 48.00 158.0 50.33 52.67 55.00 57.33 59.67 62.00 160.3 162.7 165.0 167.3 169.7 1 172.0 1 x^2 (temperature) x 1 (time) 1+ ...

factors requires 2kfactorial runs, 2kaxial runs, and at least one center point (three to five cen- ter points are typically used ...

14-20 (0, 0) ( , 0) (0, ) (–1, –1) (–1, +1) x 2 x 1 (+1, –1) (+1, +1) x 2 (– , 0) x^1 (0, – ) x 2 α α α α Figure S14-14 Central ...

14-21 48.00 158.0 50.33 52.67 55.00 57.33 59.67 62.00 160.3 162.7 165.0 167.3 169.7 172.0 Temperature Time Contour plot (a) 62.0 ...

571 CHAPTER OUTLINE LEARNING OBJECTIVES After careful study of this chapter, you should be able to do the following: Determine ...

572 CHAPTER 15 NONPARAMETRIC STATISTICS 15-1 INTRODUCTION Most of the hypothesis-testing and confidence interval procedures disc ...

15-2 SIGN TEST 573 Since the normal distribution is symmetric, the mean of a normal distribution equals the median. Therefore, t ...

574 CHAPTER 15 NONPARAMETRIC STATISTICS we should reject if the proportion of plus signs is significantly different (either less ...

15-2 SIGN TEST 575 The test statistic is the observed number of plus differences in Table 15-1, or r14. We will reject H 0 if ...

576 CHAPTER 15 NONPARAMETRIC STATISTICS The Normal Approximation When p0.5, the binomial distribution is well approximated by a ...

15-2 SIGN TEST 577 be the paired differences. We wish to test the hypothesis that the two populations have a common median, that ...

578 CHAPTER 15 NONPARAMETRIC STATISTICS 15-2.3 Type II Error for the Sign Test The sign test will control the probability of typ ...

15-2 SIGN TEST 579 If the distribution of Xhad been exponential rather than normal, the situation would be as shown in Fig. 15-1 ...

580 CHAPTER 15 NONPARAMETRIC STATISTICS 15-4. Consider the data in Exercise 15-1. Use the normal approximation for the sign test ...

15-3 WILCOXON SIGNED-RANK TEST 581 15-3 WILCOXON SIGNED-RANK TEST The sign test makes use only of the plus and minus signs of th ...

582 CHAPTER 15 NONPARAMETRIC STATISTICS Observation Differencexi 2000 Signed Rank 16 53.50  1 4 61.30  2 1 158.70  3 11  ...

15-3 WILCOXON SIGNED-RANK TEST 583 Ties in the Wilcoxon Signed-Rank Test Because the underlying population is continuous, ties a ...

584 CHAPTER 15 NONPARAMETRIC STATISTICS H 0 :  1  2 or, equivalently, H 0 : D 0 H 1 :  1  2 or, equivalently, H 1 : D ...