Exam 11: Analysis of Variance

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

SCENARIO 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that s in the 5 locations. -Referring to Scenario 11-5,the numerator and denominator degrees of freedom of the test ratio are _____ and _____ ,respectively.

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 has the same variance for the 3 brands.

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,the value of MSA is _____,while MSW is _____.

SCENARIO 11-10 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 Scenario 11-10,at 1% level of significance,

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 there is no interaction between the amount of time needed on the 3 brands of software and the 5 employees.

The Analysis of Means (ANOM)is more appropriate if you want to identify the group(s)that has(have)a higher or lower mean than the overall mean while the One-Way Analysis of Variance (One-way ANOVA)is more appropriate when you just want to see if the means of all the different groups are the same.

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,what is the value of the F test statistic for testing the block effects?

SCENARIO 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that s in the 5 locations. -Referring to Scenario 11-5,the total variation or SST is .

Which of the following is true regarding ANOVA?

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,the test is valid only if the population of crop yields has the same variance for the 3 varieties.

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,what is the value of the F test statistic for testing the block effects?

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 randomized block F test is valid only if the population of diameters is normally distributed for the 4 brands.

SCENARIO 11-10 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 Scenario 11-10,the F test statistic for testing the main effect of types of signs is

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,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 Trevor seeds.

SCENARIO 11-5 A hotel chain has identically small sized resorts in 5 locations in different small islands.The data that s in the 5 locations. -Referring to Scenario 11-5,if a level of significance of 0.05 is chosen,the null hypothesis should be rejected.

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 null hypothesis for the F test for the block effects should be rejected at a 0.01 level of significance.

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 test is valid only if the population of speeds has the same variance for the 4 brands.

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,what are the degrees of freedom of the F test statistic for testing the block effects?

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 11-9,in the context of this study,interpret the statement: "Subject visibility and test taker success interact."