382 CHAPTER 7 Hypothesis Testing with One Sample Using P@Values With t@Tests You can also use P@values for a t@test for a mean m. For instance, consider finding a P@value given t = 1.98, 15 degrees of freedom, and a right-tailed test. Using Table 5 in Appendix B, you can determine that P falls between a = 0.025 and a = 0.05 but you cannot determine an exact value for P. In such cases, you can use technology to perform a hypothesis test and find exact P@values. Using P-Values with a t-Test A department of motor vehicles office claims that the mean wait time is less than 14 minutes. A random sample of 10 people has a mean wait time of 13 minutes with a standard deviation of 3.5 minutes. At a = 0.10, test the office’s claim. Assume the population is normally distributed. SOLUTION Because s is unknown, the sample is random, and the population is normally distributed, you can use the t@test. The claim is “the mean wait time is less than 14 minutes.” So, the null and alternative hypotheses are H0: m Ú 14 minutes and Ha: m 6 14 minutes. (Claim) The TI-84 Plus display at the far left shows how to set up the hypothesis test. The two displays on the right show the possible results, depending on whether you select Calculate or Draw. From the displays, you can see that P ≈ 0.1949. Because the P@value is greater than a = 0.10, you fail to reject the null hypothesis. Interpretation There is not enough evidence at the 10% level of significance to support the office’s claim that the mean wait time is less than 14 minutes. TRY IT YOURSELF 6 Another department of motor vehicles office claims that the mean wait time is at most 18 minutes. A random sample of 12 people has a mean wait time of 15 minutes with a standard deviation of 2.2 minutes. At a = 0.05, test the office’s claim. Assume the population is normally distributed. Answer: Page A41 EXAMPLE 6 TI-84 PLUS T-Test Inpt:Data Stats μ0:14 x:13 Sx:3.5 n:10 μ:≠μ0 <μ0 >μ0 Calculate Draw TI-84 PLUS T-Test μ<14 t=-.9035079029 p=.1948994027 x=13 Sx=3.5 n=10 TI-84 PLUS t=-0.9035 p=0.1949 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. 2: T-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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