The researcher uses an a = 0.10 level of significance for the test. Therefore, the critical values for the sum of the ranks for companies with TQM implementation are TL and Tu = ▼ At the a = 0.10 level of significance, you TQM implementation and those without are the same. You companies with TQM implementation and those without. the null hypothesis that the population locations of changes in NI/S for companies with infer that there is a significant difference in NI/S performance between Suppose the researcher had a larger data set instead, consisting of 11 companies with TQM implementation and 14 companies without. The ranks for companies with TQM implementation sum to 188, and the ranks for companies without implementation sum to 137. Using the sum of ranks for companies with TQM implementation as the test statistic, the value of the corresponding z test statistic is Use the Distributions tool to help you answer the question that follows. Standard Normal Mean = 0.0 Standard Deviation = 1.0 ^ ^ ^ 0 1 2 3 4 Z The p-value for the z test statistic is At a significance level of a 0.10, you without are drawn from identical populations. You TQM implementation and those without. the null hypothesis that changes in NI/S for companies with TQM implementation and those infer that there is a significant difference in NI/S performance between companies with Total quality management (TQM) is a management approach designed to achieve continuous improvement in the quality of a company's products or services. Fundamental to the TQM approach is the need to create an awareness of quality at all levels of the organization. A researcher in a business school would like to compare the performance of companies that have implemented TQM programs with that of companies that have not. One performance measure is net income over sales (NI/S), an indicator of a company's profitability. The researcher would like to use the Wilcoxon rank sum test to determine whether the change in average NI/S is significantly different between companies with TQM implementation and companies without. Six companies were randomly selected from among those that implemented a TQM program over the same 3-year period, and four were randomly selected from among those that did not. The researcher computed each company's average quarterly NI/S for a 2-year period before the 3-year implementation period and for another 2-year period after the implementation. The change in NI/S is defined in this case as the difference between the average NI/S before and after the implementation. For each of the ten companies, the following table shows the change in NI/S and its corresponding rank. Companies with TQM Companies without TQM Company NI/S Change Rank Company NI/S Change Rank A 0.12 6 G 0.08 3 B 0.13 7 H 0.09 4 C 0.25 10 I 0.07 2 D 0.10 5 ] -0.04 1 E 0.14 8 F 0.20 9 You can assume that changes in average NI/S for the ten companies are the nonparametric alternative to the z and t tests for comparing two population means using The Wilcoxon rank sum test is The sum of the ranks for the sample of companies with TQM implementation is When the Wilcoxon rank sum test is conducted to compare two samples of sizes n₁ and П₂, the sum of ranks in the sample of size n₁ is denoted T. Its lower and upper critical values, TL, and Tu, for a one-tail test at significance level a = 0.05 or for a two-tail test at signifiance level a = 0.10 are shown in the following table. (The same information can also be found in Appendix B of your textbook, Table 9.) n1 3 4 5 6 7 8 112 TL Tu TL TU TL Tu TL T 3 6 15 11 21 16 29 23 456 N 7 17 12 24 18 32 ཥཡུཋཱ| TL TU TL Tu 37 31 46 39 57 25 33 51 42 62 ง 7 8 7 9 8 9 9 10 10 11 222225 20 13 27 19 37 26 46 35 56 14 30 20 40 28 50 37 61 24 15 33 22 43 30 54 39 66 27 16 36 24 46 32 58 41 71 29 17 39 25 50 33 63 43 76 54 31 18 42 26 54 35 67 46 80 གྲ ཀྵུ 。 པ ཥ 67 73 79 52 84 90 57 95 9 10 གྷ གྷ གླ གླ གྲུ ག ཀྵ བཻ ཌ TL Tu TL Tu 68 60 80 74 63 87 80 66 94 87 69 101 60 93 73 107 99 76 114 105 79 121 111 83 127