Exam 11: Analysis of Variance

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,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.

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

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 is normally distributed for the 3 varieties.

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,what is the null hypothesis for testing the block effects?

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

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 within group sum of squares 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,the null hypothesis for the randomized block F test for the difference in the means is

TABLE 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 Table 11-10,the F test statistic for testing the main effect of types of signs 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 mean square for the factor shape 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 are the degrees of freedom of the F test statistic for testing the block effects?

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,using an overall level of significance of 0.05,the critical range for the Tukey-Kramer procedure 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 decision made at a 0.01 level of significance on the randomized block F test for the difference in means implies that all 3 means are significantly different.

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 null hypothesis for the randomized block F test for the difference in the means should be rejected at a 0.05 level of significance.

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: -Referring to Table 11-1,the among-group (between-group)mean squares 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,the decision made at a 0.05 level of significance on the randomized block F test for the difference in means implies that all 3 means are significantly different from each other.

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 value of the test statistic is ________.

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 among-group variation or SSA 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. -Referring to Table 11-3,the null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the test statistic is greater than ________.

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 ________.

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.Which of the following tests will be the most appropriate to find out if there is any difference in crop yield among the 3 varieties?