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Chapter 9: Q92SE (page 522)

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.

a. State the null and alternative hypotheses for the ANOVA.

Short Answer

Expert verified

a. The hypothesis are given by

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3}\)

\({H_a}:{\mu _1} \ne {\mu _2} \ne {\mu _3}\).

Step by step solution

01

Given Information

The three mutual funds are given.

So, there are three treatments which are large-cap funds, medium-cap funds, and small-cap funds.

Random samples of 30 mutual funds were drawn from the three fund groups.

02

Specifying the null hypothesis

The null hypothesis are given by

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3}\)

That is all treatments are equal.

03

Specifying the alternative hypothesis

The alternative hypothesis are given by

\({H_a}:{\mu _1} \ne {\mu _2} \ne {\mu _3}\)

That is at least two treatments are not equal.

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Most popular questions from this chapter

Corporate sustainability and firm characteristics. Refer to the Business and Society (March 2011) study on how firm size and firm type impact corporate sustainability behaviors, Exercise 1.28 (p. 51). Certified Public Accountants (CPAs) were surveyed on their firms’ likelihood of reporting sustainability policies (measured as a probability between 0 and 1). The CPAs were divided into four groups depending on firm size (large or small) and firm type (public or private): large/public, large/private, small/ public, and small/private. One goal of the analysis was to determine whether the mean likelihood of reporting sustainability policies differs depending on firm size and firm type. Identify each of the following elements for this study:

a. Experimental units

b. Response variable

c. Factor(s)

d. Factor levels

e. Treatments

Value perceptions of consumers (cont’d). Refer to Exercise 9.10. In addition to the factor, Type of advertisement

(within-store price promotion and between-store price promotion), the researchers also investigated the impact of a second factor—Location where ad is read (at home or in the store). About half of the consumers who

were assigned to the within-store price promotion read the ad at home, and the other half read the ad in the store. Similarly, about half of the consumers who were assigned to the between-store price promotion read the ad at home, and the other half read the ad in the store. In this second

experiment, the goal was to compare the average discount values of the groups of consumers created by combining Type of advertisement with Location.

a. How many treatments are involved in this experiment?

b. Identify the treatments.

Identifying the type of experiment. Brief descriptions of a number of experiments are given next. Determine whether each is observational or designed and explain your reasoning.

a. An economist obtains the unemployment rate and gross state product for a sample of states over the past 10 years, with the objective of examining the relationship between the unemployment rate and the gross state product by census region.

b. A manager in a paper production facility installs one of three incentive programs in each of nine plants to determine the effect of each program on productivity.

c. A marketer of personal computers runs ads in each of four national publications for one quarter and keeps track of the number of sales that are attributable to each publication’s ad.

d. An electric utility engages a consultant to monitor the discharge from its smokestack on a monthly basis over a 1-year period to relate the level of sulfur dioxide in the discharge to the load on the facility’s generators.

e. Intrastate trucking rates are compared before and after governmental deregulation of prices changed, with the comparison also taking into account distance of haul, goods hauled, and the price of diesel fuel.

What is the difference between an observational experiment and a designed experiment?

Explain the difference between an experiment that employs a completely randomized design and one that employs a randomized block design.
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