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Figure5 - Figure 1 Comparison of(a a two-tailed test and(b...

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Unformatted text preview: Figure 1. Comparison of (a) a two-tailed test and (b) a one-tailed test, at the same probability level (95 percent). The decision of whether to use a one- or a two-tailed test is important because a test statistic that falls in the region of rejection in a one-tailed test may not do so in a two-tailed test, even though both tests use the same probability level. Suppose the class sample mean in your example was 77, and its corresponding z-score was computed to be 1.80. Table 2 in "Statistics Tables" shows the critical z- scores for a probability of 0.025 in either tail to be –1.96 and 1.96. In order to reject the null hypothesis, the test statistic must be either smaller than –1.96 or greater than 1.96. It is not, so you cannot reject the null hypothesis. Refer to Figure 1(a). Suppose, however, you had a reason to expect that the class would perform better on the proficiency...
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