Exam 11: Analysis of Variance

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 there is no significant difference between any pair of mean speeds.

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 = 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 11-4 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 null hypothesis will be rejected at a level of significance of 0.01 if the value of the test statistic is greater than __________.

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

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 = 0.05 level of significance for all inferences. -Referring to Scenario 11-12, the value of the statistic used to test for significant differences between shapes 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, what is the null hypothesis for testing the block effects?

In a two-way ANOVA, the degrees of freedom for the "error" term 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 is the value of the test statistic for Levene's test for homogeneity of variances?

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 Trevor seeds.

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 = 0.05 level of significance for all inferences. -Referring to Scenario 11-12, the value of the statistic used to test for significant differences between colors 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, the among-block variation or SSBL 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, what is the estimated relative efficiency?

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 = 0.05 level of significance for all inferences. -Referring to Scenario 11-12, based on the results of the hypothesis test, it appears that there is a significant interaction.

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. Interpret the results of the analysis summarized in the following table: -Referring to Scenario 11-2, the p-value of the test statistic for Levene's test for homogeneity of variances 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: -Referring to Scenario 11-10, the within (error)degrees of freedom 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 is the critical value of Levene's test for homogeneity of variances at a 5% 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, construct the ANOVA table from the sample data.

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 randomized block F test for the difference in the means at a level of significance of 0.01?

SCENARIO 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. -Referring to Scenario 11-5, what is the critical value of Levene's test for homogeneity of variances at a 5% 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, there is evidence of a significant difference in the mean amount of time needed to learn Brand A and Brand C at the 5% level of significance?