Question

3. Macheavellian describes negative character traits that include manipulation cunning, duplicity, deception, and bad faith. A Machiavellian ("Mach") rating score was determined for each in a random sample of 122 purchasing managers, with the following results: 8 = 99.6, s = 12.6. A director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85. a. Suppose you want to test the director's claim. Specify the null and alternative hypothesis for the test. b. Give the rejection region for the test using a = 0.10. C. Find the value of the test statistic. d. Use the result in (c) to make the appropriate conclusion.

Answer 1

(a) To perform the right-tail hypothesis test, we use the siz-step method. Step 1: The null and alternative hypotheses are as follows Ho 85 (The population mean is equal to 85) versus (The population mean is not equal to 85) Ha 85 (b) Step 2: The Decision Rule: 1.657544 We reject the null hypothesis H Otherwise, we do not reject the null hypothesis Ho We have selected a sample of n=122. We decide to use a 0.10 If the test statistic is t >to10.121 is unknown, we use the t - distributi on and the - test stati stic. Step3: Because Step4: For a given sample size, , the test stati stic follows at distribution with - degrees of freedom. The critical values of the t distribution with 122-1 =121 degrees of freedom. The table of t testis obtained by using the Excel2010 function tinv(probability, degrees of freedom) =tinv(0.10,121) =1.657544 t0.10,121 1.657544 (c) Step5 The summary stati stics: The sample mean is X = 99.6 The sample stan dard deviation is closest to s= 12.6. The sample size is n = 122 The - test stati stic is - S 99.6-85 12.6 V122 14.6 12.6 11.04536 14.6 1.14075 = 12.79859 t = 12.7986

(d) The result in part (c) can be used to estimate the p - value of the test stati stic is as follows Step6: The P- value approach: P-value 2P (t >t) 2 (1-P( <)) 2 (1-P( <12.7986) 2(1-1) 2 (0.0000) 0.0000 0.10 We reject the null hypothesis H P-value Step7: Conclusion: Since, the test statistic is t = 12.7986 ton121 =1.657544 We reject the null hypothesis Ho There is sufficient evi dence to conclude that the true mean mach rating score of all purchasing managers is not equal to 85 at the 10% level of significance.