+ D MODULE 11 - Hypothesis Testing regarding Three or More Means Using One-Way ANOVA e. Compute the MST and the MSE. AG 505 - Statistical Methods in Agriculture i. Provide formulas. Hint: Use the insert equation button from Microsoft Word to type Instructor: Dr. Jose Lopez the formulas for calculating the SST and the SSE. Click on the Insert tab, then click on the Equation button, then use the Structures buttons and the Symbols buttons from sure you submit all your answers to this lab in one Word document. the Equation Tools Design tab to type your formula. (Points: 2) ii. Show procedures. Hint: Plug in the values into the formulas provided in part (i). (Points: 4) A stock analyst wondered whether the mean rate of return of financial, energy, and utility ifi. Report the correct final answers. (Points: 4) stocks differed over the past 5 years. He obtained a simple random sample of eight companies from each of the three sectors and obtained the 5-year rates of return shown in the f. Compute the F-statistic. following table (in percent). i. Provide formula. Hint: Use the insert equation button from Microsoft Word to type the formula for calculating the SST and the SSE. Click on the Insert tab, then click on Financial Energy Utilities the Equation button, then use the Structures buttons and the Symbols buttons from the 10.76 12.72 11.88 Equation Tools Design tab to type your formula. (Points: 2) 15.05 13.91 5 86 ii. Show procedure. Hint: Plug in the values into the formula provided in part (1). 17.01 6.43 13.46 (Points: 4) 5.07 11.19 9 90 ifi. Report the correct final answer. (Points: 4) 19.50 18.79 3.95 8.16 20.73 3.44 g. Use the Microsoft Excel pre-programmed formula 0.38 9.60 7.11 =F.DIST.RT(x,deg freedoml,deg freedom2) to compute area to the right of the 6.75 17.40 15.70 F-calculated value in part (f). The F.DIST.RT pre-programmed function above has the following arguments: Source: Morningstar.com Required. The value at which to evaluate the function. This value will be the F-value you calculated in part (f). State the null and alternative hypotheses. - Deg freedom1 Required. The numerator degrees of freedom. This value In words. (Points: 5) equals k - 1, where k is the number of samples (or groups or Using the mathematical notation. (Points: 5) treatments). . Deg freedom2 Required. The denominator degrees of freedom. This value b. Compute the overall mean. You can use Microsoft Excel to compute the overall mean equals n - k, where n is the total number of observations from all three samples and & is the number of samples (or groups or and only report your answer. (Points 10) treatments). Compute the sample sizes, sample means, and sample variances and summarize your Points: 10) results in the table below. Use Microsoft Excel to do the calculations and only report h. What is the F-critical value for this hypothesis test? Use a = 0.05 significance level. your answers in the table below. (Points: 10) Hint: Use Table VIII provided in the Module 1 1 Handout to determine the critical value. (Points: 10) Groups Financial Summarize your answers in part (d), (e), (f), (g), and (h) in the ANOVA table below. Energy (Points: 10) Utilities F-Test Source of Sum of Degrees of Mean Squares Statistic P-value F-Critical d. Compute the SST and the SSE. Variation squares Freedom i. Provide formulas. Hint: Use the insert equation button from Microsoft Word to type Treatment the formulas for calculating the SST and the SSE. Click on the Insert tab, then click Error on the Equation button, then use the Structures buttons and the Symbols buttons from Total the Equation Tools Design tab to type your formula. (Points: 2) ii. Show procedures. Hint: Plug in the values into the formulas provided in part (i). State the correct conclusion for this hypothesis test ("There is sufficient evidence at the a (Points: 4) =0.05 significance level to support..." or "There is NOT sufficient evidence at the a = iii. Report the correct final answers. (Points: 4) 0.05 significance level to support..."). Make sure you state the conclusion in terms of H1. (Points: 10). w