Exam 11: Analysis of Variance

TABLE 11-11 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 US medical school graduate.The president theorizes that foreign graduates will have higher mean charges than US 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 US 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 11-11,interpret the test for interaction.

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,construct the ANOVA table from the sample data.

A completely randomized design

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. -Referring to Table 11-2,the value of the test statistic for Levene's test for homogeneity of variances is

TABLE 11-6 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomized block design,the results are presented in the table that follows. -Referring to Table 11-6,the randomized block F test is valid only if there is no interaction between the variety of seeds and the patches of fields.

TABLE 11-11 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 US medical school graduate.The president theorizes that foreign graduates will have higher mean charges than US 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 US 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 11-11,what degrees of freedom should be used to determine the critical value of the F ratio against which to test for interaction between the two factors?

TABLE 11-8 An important factor in selecting database software is the time required for a user to learn how to use the system.To evaluate three potential brands (A,B and C)of database software,a company designed a test involving five different employees.To reduce variability due to differences among employees,each of the five employees is trained on each of the three different brands.The amount of time (in hours)needed to learn each of the three different brands is given below: Below is the Excel output for the randomized block design: -In a two-way ANOVA,the degrees of freedom for the "error" term 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. -Referring to Table 11-2,the among group degrees of freedom is

TABLE 11-8 An important factor in selecting database software is the time required for a user to learn how to use the system.To evaluate three potential brands (A,B and C)of database software,a company designed a test involving five different employees.To reduce variability due to differences among employees,each of the five employees is trained on each of the three different brands.The amount of time (in hours)needed to learn each of the three different brands is given below: Below is the Excel output for the randomized block design: -Referring to Table 11-8,what is the upper-tail critical value of the Studentized range distribution for the Tukey multiple comparison procedure at the 5% level of significance?

TABLE 11-6 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomized block design,the results are presented in the table that follows. -Referring to Table 11-6,the relative efficiency means that 2.47 times as many observations in each variety group would be needed in a one-way ANOVA design as compared to the randomized block design in order to obtain the same precision for comparison of the variety means.

TABLE 11-5 A hotel chain has identically sized resorts in 5 locations.The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. -Referring to Table 11-5,the total mean squares is 261.90.

TABLE 11-7 A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow.To reduce the person-to-person variability,the students decided to use a randomized block design using themselves as blocks.Four brands of bubblegum were tested.A student chewed two pieces of a brand of gum and then blew a bubble,attempting to make it as big as possible.Another student measured the diameter of the bubble at its biggest point.The following table gives the diameters of the bubbles (in inches)for the 16 observations. -Referring to Table 11-7,what is the value of the test statistic for the randomized block F test for the difference in the means?

TABLE 11-7 A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow.To reduce the person-to-person variability,the students decided to use a randomized block design using themselves as blocks.Four brands of bubblegum were tested.A student chewed two pieces of a brand of gum and then blew a bubble,attempting to make it as big as possible.Another student measured the diameter of the bubble at its biggest point.The following table gives the diameters of the bubbles (in inches)for the 16 observations. -Referring to Table 11-7,the among-group variation or SSA is ________.

TABLE 11-12 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 11-12,the critical value in the test for a significant interaction is ________.

TABLE 11-6 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomized block design,the results are presented in the table that follows. -Referring to Table 11-6,based on the Tukey multiple comparison procedure with an overall level of significance of 0.01,the agronomist would decide that there is a significant difference between the crop yield of Smith and Walsh seeds.

A completely randomized design with 4 groups would have 6 possible pairwise comparisons.

TABLE 11-6 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds.She plants all 3 varieties of the seeds on each of 5 different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomized block design,the results are presented in the table that follows. -Referring to Table 11-6,the randomized block F test is valid only if the population of crop yields has the same variance for the 3 varieties.

TABLE 11-11 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 US medical school graduate.The president theorizes that foreign graduates will have higher mean charges than US 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 US 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 11-11,what was the total number of doctors included in the study?

TABLE 11-12 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 11-12,the mean square for the interaction of color and shape is ________.

When would you use the Tukey-Kramer procedure?