Exam 11: Analysis of Variance

SCENARIO 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 Scenario 11-2,the value of the test statistic for Levene's test for homogeneity of variances is

SCENARIO 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 Scenario 11-8,the randomized block F test is valid only if the population of the amount of time needed is normally distributed for the 3 brands.

SCENARIO 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 Scenario 11-7,the relative efficiency means that 1.0144 times as many observations in each brand 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 different means.

SCENARIO 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 Scenario 11-3,the null hypothesis should be rejected at a 5% level of significance.

In a two-factor ANOVA analysis,the sum of squares due to both factors,the interaction sum of squares and the within sum of squares must add up to the total sum of squares.

SCENARIO 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 Scenario 11-12,the value of the statistic used to test for an interaction is .

SCENARIO 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 Scenario 11-3,what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

SCENARIO 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 Scenario 11-6,the agronomist decided to perform a randomized block F test for the difference in the means.The amount of total variation or SST is .

The MSE must always be positive.

SCENARIO 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 Scenario 11-4,based on the Tukey-Kramer 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.

SCENARIO 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: -Referring to Scenario 11-1,the among-group (between-group)mean squares is

The F test statistic in a one-way ANOVA is

SCENARIO 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 Scenario 11-4,using an overall level of significance of 0.01,the critical value of the Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is .

SCENARIO 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 Scenario 11-3,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

SCENARIO 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 Scenario 11-8,it is appropriate to use the Tukey multiple comparison procedure based on the test result above.

Which of the following components in an ANOVA table are not additive?

SCENARIO 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 Scenario 11-4,based on the Tukey-Kramer 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 Walsh and Trevor seeds.

In a two-way ANOVA,the degrees of freedom for the interaction term is

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 the fewest mean number of 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 given below.How should the data be analyzed? Package 1: 12,14,9,11,16 Package 2: 2,4,7,3,1 Package 3: 10,9,6,10,12 Package 4: 7,6,6,15,12

SCENARIO 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 Scenario 11-2,the within group sum of squares is