Exam 11: Analysis of Variance

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 value of MSA is ________,while MSW is ________.

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,state the null hypothesis that can be tested.

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 mean squares is

TABLE 11-9 Psychologists have found that people are generally reluctant to transmit bad news to their peers.This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect,40 undergraduates at Duke University participated in an experiment.Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score.Unknown to the subject,the test taker was a bogus student who was working with the researchers.The experimenters manipulated two factors: subject visibility and success of test taker,each at two levels.Subject visibility was either visible or not visible to the test taker.Success of the test taker was either top 20% or bottom 20%.Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions,then the time (in seconds)between the end of the test and the delivery of the percentile score from the subject to the test taker was measured.(This variable is called the latency to feedback.)The data were subjected to appropriate analyses with the following results. -Referring to Table 11-9,what type of experimental design was employed in this study?

TABLE 11-9 Psychologists have found that people are generally reluctant to transmit bad news to their peers.This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect,40 undergraduates at Duke University participated in an experiment.Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score.Unknown to the subject,the test taker was a bogus student who was working with the researchers.The experimenters manipulated two factors: subject visibility and success of test taker,each at two levels.Subject visibility was either visible or not visible to the test taker.Success of the test taker was either top 20% or bottom 20%.Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions,then the time (in seconds)between the end of the test and the delivery of the percentile score from the subject to the test taker was measured.(This variable is called the latency to feedback.)The data were subjected to appropriate analyses with the following results. -Referring to Table 11-9,in the context of this study,interpret the statement: "Subject visibility and test taker success interact."

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,at a significance level of 1%,

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 within groups degrees of freedom 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,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

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 null hypothesis 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 null hypothesis for the randomized block F test for the difference in the means should be rejected at a 0.01 level of significance.

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 amount of total variation or SST is ________.

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 critical value of the randomized block F test for the difference in the means at a level of significance of 0.05?

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 Walsh and Trevor seeds.

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 test is less sensitive to the assumption that the population of speeds has the same variance for the 4 brands because the sample sizes of the 4 brands are equal.

If you are comparing the mean sales among 3 different brands you are dealing with a three-way ANOVA design.

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

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 are the degrees of freedom of the F test statistic 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,the agronomist decided to perform a randomized block F test for the difference in the means.The amount of total variation or SST 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 value of the statistic used to test for an interaction 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 randomized block F test is valid only if the population of the amount of time needed has the same variance for the 3 brands.