380 CHAPTER 8 Hypothesis Testing To find the P-value, first find the area beyond the test statistic, (using technology or Table A-2), then use the procedure given in Figure 8-3. That procedure can be summarized as follows: ■ Critical region in left tail: P@value = area to the left of the test statistic ■ Critical region in right tail: P@value = area to the right of the test statistic ■ Critical region in two tails: P@value = twice the area in the tail beyond the test statistic P-Value Method With the P-value method of testing hypotheses, we make a decision by comparing the P-value to the significance level. DEFINITION In a hypothesis test, the P-value is the probability of getting a value of the test statistic that is at least as extreme as the test statistic obtained from the sample data, assuming that the null hypothesis is true. CAUTION Don’t confuse the following notation: • P@value = probability of getting a test statistic at least as extreme as the one found from the sample data, assuming that the null hypothesis H0 is true • p = population proportion • pn = sample proportion P-value P-value is twice this area. Test statistic Test statistic Test statistic Test statistic P-value is twice this area. P-value Is the test statistic to the right or left of center? Left Right Left-tailed Right-tailed Two-tailed P-value 5 twice the area to the left of the test statistic P-value 5 area to the left of the test statistic P-value 5 twice the area to the right of the test statistic P-value 5 area to the right of the test statistic What type of test? Start FIGURE 8-3 Finding P-Values
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