408 CHAPTER 8 Hypothesis Testing Examine the technology displays to see that only two of them include critical values, but they all include P-values. This is a major reason why the P-value method of testing hypotheses has become so widely used in recent years. P-Value Method Without Technology If suitable technology is not available, we can use Table A-3 to identify a range of values containing the P-value. In using Table A-3, keep in mind that it is designed for positive values of t and right-tail areas only, but left-tail areas correspond to the same t values with negative signs. StatCrunch Minitab JMP SPSS Adult Sleep: P-Value Method Without Technology EXAMPLE 2 Example 1 is a left-tailed test with a test statistic of t = -0.290 (rounded) and a sample size of n = 12, so the number of degrees of freedom is df = n - 1 = 11. Using the test statistic of t = -0.290 with Table A-3, examine the values of t in the row for df = 11 to see that 0.290 is less than all of the listed t values in the row, which indicates that the area in the left tail below the test statistic of t = -0.290 is greater than 0.10. In this case, Table A-3 allows us to conclude that P@value 7 0.10, but technology provided the P@value of 0.3887. With the P@value 7 0.10, the conclusions are the same as in Example 1. YOUR TURN. Do Exercise 21 “Lead in Medicine.” HINT Because using Table A-3 to find a range of values containing the P-value can be a bit tricky, the critical value method (see Example 3) might be easier than the P-value method if suitable technology is not available. M Holistic Statistics Instead of using only the P-value method of testing a claim about a population mean, it is wise to use holistic statistics with a variety of different approaches. Begin with an analysis of the sampling method, and explore the sample data looking for outliers, the nature of the distribution, and anything else notable about the data. In addition to the t-test described in this section, construct a confidence interval (Section 7-2), use the sign test (Section 13-2), Wilcoxon SignedRanks test (Section 13-3), use bootstrapping to obtain a confidence interval estimate of the population mean (Section 7-4), and use the resampling method of randomization (Section 8-5). This holistic approach is much more likely to provide us with clear understanding of the claim being tested. See Chapter 15. I u t m t a la
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