Answer the following questions with explanation

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. Source df SS MS F p-Value 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. J. 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 directmail company assembles and stores paper products l'envelopes. letters. brochures, order cards. etc.)I 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. a. Identify the response, t'actorls), 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 fI'OITI one carton 01' from man)\" cartons