a. Compute the sum of squares between treatments.
b. Compute the mean square between treatments.
c. Compute the sum of squares due to error.
d. Compute the mean square due to error.
e. Set up the ANOVA table for this problem.
f. At the α = .05 level of significance, test whether the means for the three treatments are equal.
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13.2 In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table....
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13.3 Refer to exercise 2.
a. What hypotheses are implied in this problem?
b. At the α = .05 level of significance, can we reject the null hypothesis in part (a)? Explain.
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13.4 In an experiment designed to test the output levels of three different treatments, the following results were obtained: SST = 400, SSTR = 150, nT = 19. Set up the ANOVA table and test for any significant difference between the mean output levels of the three treatments. Use α = .05.
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13.5 In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?...
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13.6 Develop the analysis of variance computations for the following completely randomized design. At α = .05, is there a significant difference between the treatment means?...
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13.7 Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4560.
a. Set up the ANOVA table for this problem.
b. Use α = .05 to test for any significant difference in the means for the three assembly methods.
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13.8 Refer to the NCP data in Table 13.4. Set up the ANOVA table and test for any significant difference in the mean examination score for the three plants. Use α = .05.
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13.9 To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process....
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13.10 Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study, auditors were asked to make judgments about the frequency of errors to be found in an audit. The judgments by the auditors were then compared to the actual results. Suppose the following data were obtained from a similar study; lower scores indicate better judgments....Use α = .05 to test to see whether the basis for the judgment affects the quality of the judgment.What is your conclusion?
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13.11 Four different paints are advertised as having the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained....At the α = .05 level of significance, test to see whether the mean drying time is the same for each type of paint.
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13.12
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13.13 The following data are from a completely randomized design....
a. At the α = .05 level of significance, can we reject the null hypothesis that the means of the three treatments are equal?
b. Use Fisher’s LSD procedure to test whether there is a significant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use α = .05.
c. Use Fisher’s LSD procedure to develop a 95% confidence interval estimate of the difference between the means of treatments A and B.
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13.14 The following data are from a completely randomized design. In the following calculations, use α = .05....
a. Use analysis of variance to test for a significant difference among the means of the three treatments.
b. Use Fisher’s LSD procedure to determine which means are different.
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13.15 To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material....
a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use α = .05.
b. At the α = .05 level of significance, use Fisher’s LSD procedure to test for the equality of the means for manufacturers 1 and 3. What conclusion can you draw after carrying out this test?
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13.16 Refer to exercise 15. Use Fisher’s LSD procedure to develop a 95% confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2.
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13.17 The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical values)....
a. Use α = .05 to test for significant differences in perception among the three groups.
b. At the α = .05 level of significance, we can conclude that there are differences in the perceptions for marketing managers, marketing research specialists, and advertising specialists. Use the procedures in this section to determine where the differences occur. Use α = .05.
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13.18 To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained....
a. At the α = .05 level of significance, what is the difference, if any, in the population mean times among the four machines?
b. Use Fisher’s LSD procedure to test for the equality of the means for machines 2 and 4. Use a .05 level of significance.
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13.19 Refer to exercise 18. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment wise error rate of .05 is desired.
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13.20
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13.21 Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table....Use α = .05 to test for any significant differences.
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13.22 The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 430, SSTR = 310, SSBL = 85. Set up the ANOVA table and test for any significant differences. Use α = .05.
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13.23 An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table....Use α = .05 to test for any significant differences.
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13.24 An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow....Use α = .05 to test for any significant differences.
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13.25 Prices for vitamins and other health supplements increased over the past several years, and the prices charged by different retail outlets often vary a great deal. The following data show the prices for 13 products at four retail outlets in Rochester, New York [Rochester Democrat and Chronicle, February 13, 2005]....Use α = .05 to test for any significant difference in the mean price for the four retail outlets.
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13.26
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13.27 A study reported in the Journal of the American Medical Association investigated the cardiac demands of heavy snow shoveling. Ten healthy men underwent exercise testing with a treadmill and a cycle ergo meter modified for arm cranking. The men then cleared two tracts of heavy, wet snow by using a lightweight plastic snow shovel and an electric snow thrower. Each subject’s heart rate, blood pressure, oxygen uptake, and perceived exertion during snow removal were compared with the values obtained during treadmill and arm-crank ergometer testing. Suppose the following table gives the heart rates in beats per minute for each of the 10 subjects....At the .05 level of significance, test for any significant differences.
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13.28 A factorial experiment involving two levels of factor A and three levels of factor B resulted in the following data....Test for any significant main effects and any interaction. Use α = .05.
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13.29 The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 280, SSA = 26, SSB = 23, SSAB = 175. Set up the ANOVA table and test for any significant main effects and any interaction effect. Use α = .05.
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13.30 A mail-order catalog firm designed a factorial experiment to test the effect of the size of a magazine advertisement and the advertisement design on the number of catalog requests received (data in thousands). Three advertising designs and two different-size advertisements were considered. The data obtained follow. Use the ANOVA procedure for factorial designs to test for any significant effects due to type of design, size of advertisement, or interaction. Use α = .05....
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13.31 An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05....
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13.32
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13.33 A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of 1336 key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained 19 relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher’s search for relevant key words. Subjects in the low time pressure situation were told they had 25 minutes to complete the problem, an amount of time which should be “more than adequate” to complete the case; subjects in the moderate time pressure situation were told they would have “only” 11 minutes to complete the case. Suppose 25 subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses)....Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a .05 level of significance. Assume that the total sum of squares for this experiment is 327.50.
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13.34 In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?...
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13.35 A study reported in the Journal of Small Business Management concluded that self-employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1–5 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18–90, is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow....At the α = .05 level of significance, test for any difference in the job satisfaction among the four professions.
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13.36 Money magazine reports percentage returns and expense ratios for stock and bond funds. The following data are the expense ratios for 10 midcap stock funds, 10 small-cap stock funds, 10 hybrid stock funds, and 10 specialty stock funds (Money, March 2003)....Use α = .05 to test for any significant difference in the mean expense ratio among the four types of stock funds.
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13.37
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13.38 Three different assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly selected and assigned to use one of the proposed methods. The number of units produced by each worker follows....Use these data and test to see whether the mean number of parts produced is the same with each method. Use α = .05.
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13.39 In a study conducted to investigate browsing activity by shoppers, each shopper was initially classified as a non browser, light browser, or heavy browser. For each shopper, the study obtained a measure to determine how comfortable the shopper was in a store. Higher scores indicated greater comfort. Suppose the following data were collected....
a. Use α = .05 to test for differences among comfort levels for the three types of browsers.
b. Use Fisher’s LSD procedure to compare the comfort levels of non browsers and light browsers. Use α = .05. What is your conclusion?
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13.40 A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow....
a. At α = .05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline?
b. Analyze the experimental data using the ANOVA procedure for completely randomized designs. Compare your findings with those obtained in part (a). What is the advantage of attempting to remove the block effect?
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13.41 Wegman’s Food Markets and Tops Friendly Markets are the major grocery chains in the Rochester, New York, area. When Wal-Mart opened a Supercenter in one of the Rochester suburbs, experts predicted that Wal-Mart would undersell both local stores. The Rochester Democrat and Chronicle obtained the price data in the following table for a 15-item market basket [Rochester Democrat and Chronicle, March 17, 2002]....At the .05 level of significance, test for any significant difference in the mean price for the 15-item shopping basket for the three stores.
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13.42 The U.S. Department of Housing and Urban Development provides data that show the fair market monthly rent for metropolitan areas. The following data show the fair market monthly rent ($) in 2005 for one-bedroom, two-bedroom, and three-bedroom apartments for five metropolitan areas (The New York Times Almanac, 2006)....At the .05 level of significance, test whether the mean fair market monthly rent is the same for each metropolitan area.
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13.43 A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours....Test for any significant differences due to language translator, type of language, and interaction. Use α = .05.
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13.44 A manufacturing company designed a factorial experiment to determine whether the number of defective parts produced by two machines differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system. The following data give the numbers of defective parts produced. Use α =.05 to test for any significant effect due to machine ,loading system, and interaction....Compensation for Sales ProfessionalsSuppose that a local chapter of sales professionals in the greater San Francisco area conducted a survey of its membership to study the relationship, if any, between the years of experience and salary for individuals employed in inside and outside sales positions. On the survey, respondents were asked to specify one of three levels of years of experience: low (1-10 years), medium (11-20 years), and high (21 or more years). A portion of the data obtained follows. The complete data set, consisting of 120 observations, is available on the CD accompanying the text in the file named Sales Salary....
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