MODULE 12 - Post Hoc Tests on One-Way Analysis of Variance AG 505 - Statistical Methods in Agriculture Instructor: Dr. Jose Lopez Make sure you submit all your answers to this lab in one Word document. 1. One measure of the value of a stock is its price to earnings ratio (or P/E ratio). It is the ratio of the price of a stock per share to the earnings per share and can be thought of as the price an investor is willing to pay for $1 of earnings in a company. A stock analyst wants to know whether the P/E ratios for three industry categories differ significantly. The following data represent simple random samples of companies from three categories: (1) financial, (2) food, and (3) leisure goods. Financial Food Leisure Goods 3.83 19.75 14.10 12.75 17.87 10.12 13.48 15.18 15.57 14.42 22.84 13.48 10.06 15.60 11.27 Source: Yahoo!Finance. (a) Use Microsoft Excel Data Analysis ToolPak to test the null hypothesis that the mean P/E ratio for each category is the same at the a = 0.05 level of significance. Note: The requirements for a one-way ANOVA are satisfied. (i) State the null and alternative hypotheses. (Points: 5) HO: u1 = 12 = Us . H1: un # uz # us (i) Copy and paste the SUMMARY table from the worksheet ply containing the results in your Word document. (Points: 10) Anova: Single Factor Page 1 of 3SUMMARY Groups Count Sum Average Variance Column 1 5 59.54 11.908 5.59487 Column 2 91.24 18.248 9.97747 Column 3 64.54 12.908 4.82257 (ii) Copy and paste the ANOVA table from the worksheet ply containing the results in your Word document. (Points: 10) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 59.54 11.908 5.59487 Column 2 91.24 18.248 9.97747 Column 3 64.54 12.908 4.82257 ANOVA Source of 55 MS F P-value F crit Variation Between 116.185333 2 58.0926667 8.54517132 0.00492713 3.88529383 Groups Within 81.57964 12 6.79830333 Groups Total 197.764973 14 Page 2 of 3(iii)State the correct conclusion for this hypothesis test ("There is sufficient evidence at the a = 0.05 significance level to support..." or "There is NOT sufficient evidence at the a = 0.05 significance level to support..."). Make sure you state the conclusion in terms of Hi. (Points: 5) . Reject HO, F statistic does not fall into perimeters of F critical. (b) If the null hypothesis is rejected in part (a), use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05. (1) Write down the sample means in ascending order. (Points: 5) (2) Compute the pairwise differences for each pair of sample means. (Points: 5) (3) Compute the Tukey's test statistic for each pairwise difference for each pair of sample means. (Points: 5) (4) Determine the critical value. (Points: 5) (5) For each pair of sample means, state whether you reject or fail to reject the null hypothesis. Make sure you clearly state for which pair you reject or fail to reject the null hypothesis. (Points: 5) (6) Summarize the conclusions of Tukey's test in a figure by underlining the populations means which are not significantly different from each other. (Points: 5) (c) Draw boxplots of the three categories to support the analytic results obtained in parts (a) and (b). Don't forget to double check the whiskers of each boxplots. (i) Adjust the horizontal axis of each boxplot so that all three boxplots horizontal axes begin at the same value and ends at the same value. Hint: For an example, see the boxplots reported in Example 1 of the Module 11 Handout. (Points: 5) (ii) Copy and paste each boxplot in your word document. (Points: 10 per boxplot) (iii) Do the boxplots support the analytic results in part (a) and (b)? Make sure you explain why/how the boxplots support the analytic results from part (a) and (b). (Points: 5) Page 3 of 3