Question

A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.9 55.6 39.4 43.8 24.7 37.5 32.3 41.3 10.9 27.3 29.3 32.3 38.5 39.3 15.2 36.2 42.5 20.6 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use a 1% level of significance. (a) What is the level of significance? Correct: Your answer is correct. State the null and alternate hypotheses. Ho: μ1 = μ2 = μ3; H1: Not all the means are equal. Ho: μ1 = μ2 = μ3; H1: All three means are different. Ho: μ1 = μ2 = μ3; H1: Exactly two means are equal. Ho: μ1 = μ2 = μ3; H1: At least two means are equal. Correct: Your answer is correct. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001 Incorrect: Your answer is incorrect. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value is greater than the level of significance at α = 0.01, we do not reject H0. Since the P-value is less than or equal to the level of significance at α = 0.01, we reject H0. Since the P-value is greater than the level of significance at α = 0.01, we reject H0. Since the P-value is less than or equal to the level of significance at α = 0.01, we do not reject H0. Correct: Your answer is correct. (e) Interpret your conclusion in the context of the application. At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal. At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal. At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal. Correct: Your answer is correct. (f) Make a summary table for your ANOVA test. Source of Variation Sum of Squares Degrees of Freedom MS F Ratio P Value Test Decision Between groups Correct: Your answer is correct. Correct: Your answer is correct. Within groups Total

Answer 1

2 4249O 55.6803 34 152. 438 849- 63.5 406-25 32.3 1043-3 27-3 145-30-3 858-uq 82.3 38-5 482.3 36 1310 04 20.6 2u4 118-8 41 3 105.7 I0 3.3 1544-5152 231. 04 4 2.5 1806-25 6158 05 XTOT 616.6 TOT23338.31

Standar ć deviaron 'Tue rul hypotnes Ưlfalg tta, all ナ Sample r oups Come row gup poplationau equal level a 8gnifian

TOr TOT TOt TOT 24 y, 6 t lqo.2 t m. 616-6 q370 24 t 7810.08 t 6158 .OS 2333& 3 616.6 23338-3) TOT 28338.37-2t121.a SStor 1216. 3 Meon 0f al x value! хтот TOT 6166 1& 34.95

Twerefore, tw between gout Vanatun 616 6- 34.25 5Sge 5823 9916-3 ← 582.3s eqre es of sreedom dd betI e.no aqo 8-1 18-3

M S SSBET 531.-35, 2qi-H 582 3S 2 ds BET 6633.qS (5 442.26 d. 291 1 HU2.2С M5BET MSW : 0 658 de nomrncdor 15 띠 Pr Value =0.532, ince tuç alue eater 60 wedo not reject null hypotner thejii (Ho )

Jutficien eridece to Condude tna al ANOVA YEST Ource Mf Jest Of ariaion Belaee 582.3526 0 5322 S 0 6 633.q5 15 442-26 within roup 7216.3 I7 33 43