368 CHAPTER 7 Hypothesis Testing with One Sample Left-Tailed Test z 0 α z 0 Right-Tailed Test z 0 α z 0 Two-Tailed Test z 0 α −z 0 z 0 1 2 α 1 2 Using Technology to Find a P-Value Use the TI-84 Plus displays to make a decision to reject or fail to reject the null hypothesis at a level of significance of a = 0.05. TI-84 PLUS Z-Test Inpt:Data Stats μ0:6.2 s:.47 x:6.07 n:53 μ:≠μ0 <μ0 >μ0 Calculate Draw TI-84 PLUS Z-Test μ≠6.2 z=-2.013647416 p=.0440464253 x=6.07 n=53 SOLUTION The P@value for this test is 0.0440464253. Because the P@value is less than a = 0.05, you reject the null hypothesis. TRY IT YOURSELF 6 Repeat Example 6 using a level of significance of a = 0.01. Answer: Page A41 Rejection Regions and Critical Values Another method to decide whether to reject the null hypothesis is to determine whether the standardized test statistic falls within a range of values called the rejection region of the sampling distribution. A rejection region (or critical region) of the sampling distribution is the range of values for which the null hypothesis is not probable. If a standardized test statistic falls in this region, then the null hypothesis is rejected. A critical value z0 separates the rejection region from the nonrejection region. DEFINITION Finding Critical Values in the Standard Normal Distribution 1. Specify the level of significance a. 2. Determine whether the test is left-tailed, right-tailed, or two-tailed. 3. Find the critical value(s) z0. When the hypothesis test is a. left-tailed, find the z@score that corresponds to an area of a. b. right-tailed, find the z@score that corresponds to an area of 1 - a. c. two-tailed, find the z@scores that correspond to 1 2a and 1 - 1 2a. 4. Sketch the standard normal distribution. Draw a vertical line at each critical value and shade the rejection region(s). (See the figures at the left.) GUIDELINES Note that a standardized test statistic that falls in a rejection region is considered an unusual event. EXAMPLE 6 Tech Tip Using a TI-84 Plus, you can either enter the original data into a list to find a P@value or enter the descriptive statistics. STAT Choose the TESTS menu. 1: Z-Test... Select the Data input option when you use the original data. Select the Stats input option when you use the descriptive statistics. In each case, enter the appropriate values including the corresponding type of hypothesis test indicated by the alternative hypothesis. Then select Calculate.
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