Exam 11: Analysis of Variance

TABLE 11-3 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. -Referring to Table 11-3,in testing the null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal,the value of the test statistic is ________.

TABLE 11-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each,as shown below. A: 1.2,1.1,0.9,0.4 C: 1.0,1.5,1.1,1.3 B: 2.5,2.1,1.9,1.6 D: 0.8,1.3,1.1,0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 11-2,the critical value of Levene's test for homogeneity of variances at a 5% level of significance is

TABLE 11-9 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal.He combined 4 colors and 3 shapes to produce a total of 12 designs.Each logo was presented to 2 different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analyzed these data using the α = 0.05 level of significance for all inferences. -Which of the following is an assumption required by the Analysis of Means (ANOM)?

TABLE 11-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each,as shown below. A: 1.2,1.1,0.9,0.4 C: 1.0,1.5,1.1,1.3 B: 2.5,2.1,1.9,1.6 D: 0.8,1.3,1.1,0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 11-2,the among group degrees of freedom is

TABLE 11-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each,as shown below. A: 1.2,1.1,0.9,0.4 C: 1.0,1.5,1.1,1.3 B: 2.5,2.1,1.9,1.6 D: 0.8,1.3,1.1,0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 11-2,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

TABLE 11-8 A physician and president of a Tampa Health Maintenance Organization (HMO)are attempting to show the benefits of managed health care to an insurance company.The physician believes that certain types of doctors are more cost-effective than others.One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians.To investigate this,the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP),Internal Medicine (IM),Pediatrics (PED),and Family Physicians (FP)- and recorded the total charges per member per month for each.A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate.The president theorizes that foreign graduates will have higher mean charges than USA graduates.To investigate this,the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above.So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates)was obtained for each of the 4 specialties.The results for the ANOVA are summarized in the following table. -Referring to Table 11-8,interpret the test for interaction.

TABLE 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. Analysis of Variance * or p < 0.005,tabular value -Referring to Table 11-5,what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

TABLE 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. Analysis of Variance * or p < 0.005,tabular value -Referring to Table 11-5,the among-group variation or SSA is ________.

TABLE 11-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each,as shown below. A: 1.2,1.1,0.9,0.4 C: 1.0,1.5,1.1,1.3 B: 2.5,2.1,1.9,1.6 D: 0.8,1.3,1.1,0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 11-2,the within group mean squares is

TABLE 11-4 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants 15 fields,5 with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomized design,the results are presented in the table that follows. -True or False: Referring to Table 11-4,the test is valid only if the population of crop yields is normally distributed for the 3 varieties.

TABLE 11-9 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal.He combined 4 colors and 3 shapes to produce a total of 12 designs.Each logo was presented to 2 different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analyzed these data using the α = 0.05 level of significance for all inferences. -Referring to Table 11-9,the value of the statistic used to test for an interaction is ________.

TABLE 11-3 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. -True or False: Referring to Table 11-3,the test is less sensitive to the assumption that the population of speeds has the same variance for the 4 brands because the sample sizes of the 4 brands are equal.

TABLE 11-6 Psychologists have found that people are generally reluctant to transmit bad news to their peers.This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect,40 undergraduates at Duke University participated in an experiment.Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score.Unknown to the subject,the test taker was a bogus student who was working with the researchers.The experimenters manipulated two factors: subject visibility and success of test taker,each at two levels.Subject visibility was either visible or not visible to the test taker.Success of the test taker was either top 20% or bottom 20%.Ten subjects were randomly assigned to each of the 2 × 2 = 4 experimental conditions,then the time (in seconds)between the end of the test and the delivery of the percentile score from the subject to the test taker was measured.(This variable is called the latency to feedback.)The data were subjected to appropriate analyses with the following results. -Referring to Table 11-6,in the context of this study,interpret the statement: "Subject visibility and test taker success interact."

TABLE 11-7 A campus researcher wanted to investigate the factors that affect visitor travel time in a complex,multilevel building on campus.Specifically,he wanted to determine whether different building signs (building maps versus wall signage)affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building.Three subjects were assigned to each of the combinations of signs and starting locations,and travel time in seconds from beginning to destination was recorded.An Excel output of the appropriate analysis is given below: ANOVA -Referring to Table 11-7,the within (error)degrees of freedom is

TABLE 11-4 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants 15 fields,5 with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomized design,the results are presented in the table that follows. -Referring to Table 11-4,the agronomist decided to compare the 3 treatment means by using the Tukey-Kramer procedure with an overall level of significance of 0.01.There are ________ pairwise comparisons that can be made.

TABLE 11-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each,as shown below. A: 1.2,1.1,0.9,0.4 C: 1.0,1.5,1.1,1.3 B: 2.5,2.1,1.9,1.6 D: 0.8,1.3,1.1,0.7 Interpret the results of the analysis summarized in the following table: -Referring to Table 11-2,the p-value of the test statistic for Levene's test for homogeneity of variances is

True or False: The analysis of variance (ANOVA)tests hypotheses about the population variance.

TABLE 11-1 An airline wants to select a computer software package for its reservation system.Four software packages (1,2,3,and 4)are commercially available.The airline will choose the package that bumps as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks.(A total of 20 weeks was included in the experiment.)The number of passengers bumped each week is obtained,which gives rise to the following Excel output: ANOVA -Referring to Table 11-1,the among-group (between-group)mean squares is

TABLE 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. Analysis of Variance * or p < 0.005,tabular value -Referring to Table 11-5,what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

TABLE 11-9 The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal.He combined 4 colors and 3 shapes to produce a total of 12 designs.Each logo was presented to 2 different groups (a total of 24 groups)and the approval rating for each was recorded and is shown below.The manager analyzed these data using the α = 0.05 level of significance for all inferences. -True or False: Referring to Table 11-9,based on the results of the hypothesis test,it appears that there is a significant effect on the approval rating associated with the color of the logo.