Mutual Fund Performance Analysis: ANOVA Study Insights

Assignment 10 — Problems 9.92 STUDY OF MUTUAL FUND PERFORMANCE. Mutual funds are classified as large-cap funds, medium-cap funds, or small-cap funds, depending on the capitalization of the companies in the fund. Hawaii Pacific University researchers investigated whether the average performance of a mutual fund is related to capitalization size (American Business Review, January 2002). Independent random samples of 30 mutual funds were selected from each of the three fund groups, and the 90-day rate of return was determined for each fund. The data for the 90 funds were subjected to an analysis of variance, with the results shown in the ANOVA summary table below. Fund group 2 409.566 204.783 6.965 .002 Error 87 2,557.860 29.401 Total 89 2,967.426 Source: S. W. Shi and M. ]. Seiler, “Growth and Value Style Comparison of U.S. Stock Mutual Funds,” American Business Review, January 2002 (Table 3). Published by American Business Review, © 2002. a. State the null and alternative hypotheses for the ANOVA. b. Give the rejection region for the test using a = .01. c. Make the appropriate conclusion using either the test statistic or the p-value.

9.98 [Data Set: CARTON] A MANAGERIAL DECISION PROBLEM. A direct-mail company assembles and stores paper products (envelopes, letters, brochures, order cards, etc.) for its customers. The company estimates the total number of pieces received in a shipment by estimating the weight per piece and then weighing the entire shipment. The company is unsure whether the sample of pieces used to estimate the mean weight per piece should be drawn from a single carton, or whether it is worth the extra time required to pull a few pieces from several cartons. To aid management in making a decision, eight brochures were pulled from each of five cartons of a typical shipment and weighed. The weights (in pounds) are shown in the table. .01851 .01872 .01869 .01899 .01882 .01829 .01861 .01853 01917 .01895 .01844 .01876 .01876 .01852 .01884 .01859 .01886 .01880 .01904 .01835 .01854 .01896 .01880 .01923 .01889 .01853 .01879 .01882 .01905 .01876 .01844 .01879 .01862 .01924 .01891 .01833 .01879 .01860 .01893 .01879 a. Identify the response, factor(s), treatments, and experimental units. b. Do these data provide sufficient evidence to indicate differences in the mean weight per brochure among the five cartons? c. What assumptions must be satisfied in order for the test of part b to be valid? d. Use Tukey’s method to compare all pairs of means, with a = .05 as the overall level of significance. e. Given the results, make a recommendation to management about whether to sample from one carton or from many cartons.

9.52 [Data Set: L09052] A randomized block design was used to compare the mean responses for three treatments. Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to one experimental unit within each block. The data are shown below, followed by a StatCrunch ANOVA printout for this experiment. A 3.4 55 7.9 1.3 B 4.4 5.8 9.6 2.8 C 2.2 3.4 6.9 3 Two Way Analysis of Variance results: Responses: RESPONSE Row factor: TREATMENT Column factor: BLOCK ANOVA table Source DF SS MS P-value TREATMENT 2 12.031667 6.0158333 50.957647 0.00021 jBLOCK 3| 71749167 23.916389 202.58588 | <0.0001 jError 6 0.70833333 0.11805556 ' Total 11 84.489167 Tukey HSD results (95% level) for TREATMENT: A subtracted from Difference } Lower 7 P-value B 1125 037954331 1.8704567 0.0085 € -1325| -2.0704567 -0.57954331 0.0038 B subtracted from Difference Lower C 245 -3.1954567 Upper I P-value ‘ -1.7045433 0.0001

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a. Use the printout to fill in the entries in the following ANOVA table. Treatments Blocks Error Total b. Do the data provide sufficient evidence to indicate that the treatment means differ? Use a = .05. c. Do the data provide sufficient evidence to indicate that blocking was effective in reducing the experimental error? Use a = .05. d. Use the printout to rank the treatment means at a = .05. e. What assumptions are necessary to ensure the validity of the inferences made in parts b, ¢, and d?

9.104 [Data Set: WALKS] PARTICIPATION IN A COMPANY'S WALKING PROGRAM. A study was conducted to investigate the effect of prompting in a walking program instituted at a large corporation (Health Psychology, March 1995). Five groups of walkers—27 in each group—agreed to participate by walking for 20 minutes at least one day per week over a 24-week period. The participants were prompted to walk each week via telephone calls, but different prompting schemes were used for each group. Walkers in the control group received no prompting phone calls; walkers in the “frequent/low” group received a call once a week with low structure (i.e., “just touching base”); walkers in the “frequent/high" group received a call once a week with high structure (i.e., goals are set); walkers in the “infrequent/low” group received a call once every 3 weeks with low structure; and walkers in the “infrequent/high” group received a call once every 3 weeks with high structure. The table below lists the number of participants in each group who actually walked the minimum requirement each week for weeks 1, 4, 8, 12, 16, and 24. The data were subjected to an analysis of variance for a randomized block design, with the five walker groups representing the treatments and the six time periods (weeks) representing the blocks. Prompt 4 1185.000 — — 0.0000 Week = 386.400 77.28000 10.40 0.0001 Error 20 148.600 7.43000 Totals 29 1720.00 a. What is the purpose of blocking on weeks in this study? b. Fill in the missing entries on the ANOVA summary table shown. c. Is there sufficient evidence of a difference in the mean number of walkers per week among the five walker groups? Use a = .05. Table for Exercise 9.10418

Frequent/High Infrequent/High 1 7 23 25 21 19 - 2 19 25 10 12 8 2 18 19 9 9 12 2 7 20 8 2 16 2 18 18 8 7 24 1 17 17 7 6 Source: D. N. Lombard, T. N. Lombard, and R. A. Winett, “Walking to Meet Health Guidelines: The Effect of Prompting Frequency and Prompt Structure,” Health Psychology, Vol. 14, No. 2, March 1995, p. 167 (Table 2). Turkey Ranking for Exercise 9.10418 Mean: 2.67 9.17 10.50 17.00 20.67 Prompt: Control Infr./High Infr./Low Frequent/Low Frequent/High d. Tukey's technique was used to compare all pairs of treatment means with an experimentwise error rate of a = .05. The rankings are shown above. Interpret these results. e. What assumptions must hold to ensure the validity of the inferences in parts ¢ and d?

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Assignment 10 - QUESTIONS

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