Section 9.3 Hypothesis Tests for a Population Mean, Standard Deviation Unknown 443 EXCEL Testing a hypothesis about a population mean when �� is unknown This procedure requires the MegaStat EXCEL add-in to be loaded. The MegaStat add-in can be downloaded from www.mhhe.com/megastat. Step 1. Load the MegaStat EXCEL add-in. Step 2. Click on the MegaStat menu and select Hypothesis Tests, then Mean vs. Hypothesized Value... Step 3. Choose one of the following: ∙ If the summary statistics are given, choose summary input and enter the range of the cells that contains, in the following order, the variable name, ̄x, s, and n. ∙ If the raw data are given, choose data input and select the range of cells that contains the data in the Input Range field. For Example 9.17, the sample has been entered in column A (Figure E). Step 4. Enter the Hypothesized mean (3.5) and select the form of the alternate hypothesis (not equal). Step 5. Choose the t-test option (Figure F). Step 6. Click OK (Figure G) Figure E Figure F Figure G SECTION 9.3 Exercises Exercises 1– 6 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 7 and 8, fill in each blank with the appropriate word or phrase. 7. To perform a t-test when the sample size is small, the sample must show no evidence of strong and must contain no . skewness, outliers 8. The number of degrees of freedom for the Student’s t-test of a population mean is always 1 less than the . sample size In Exercises 9 and 10, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 9. A t-test is used when the population standard deviation is unknown. True 10. A t-test is used when the number of degrees of freedom is unknown. False Practicing the Skills 11. Find the P-value for the following values of the test statistic t, sample size n, and alternate hypothesis H1. If you use Table A.3, you may specify that P is between two values. a. t = 2.336, n = 5, H1: �� > ��0 0.0399 b. t = 1.307, n = 18, H1: �� ≠ ��0 0.2086 c. t = −2.864, n = 51, H1: �� < ��0 0.0030 d. t = −2.031, n = 3, H1: �� ≠ ��0 0.1793 12. Find the P-value for the following values of the test statistic t, sample size n, and alternate hypothesis H1. If you use Table A.3, you may specify that P is between two values. a. t = −1.584, n = 19, H1: �� ≠ ��0 0.1306 b. t = −2.473, n = 41, H1: �� < ��0 0.0089 c. t = 1.491, n = 30, H1: �� ≠ ��0 0.1468 d. t = 3.635, n = 4, H1: �� > ��0 0.0179 13. Find the critical value or values for the following values of the significance level ��, sample size n, and alternate hypothesis H1. a. �� = 0.05, n = 27, H1: �� ≠ ��0 −2.056, 2.056 b. �� = 0.01, n = 61, H1: �� > ��0 2.390
navidi_monk_elementary_statistics_2e_ch7-9
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