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Exam 11: Analysis of Variance

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Question 111

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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,what is the value of the test statistic for Levene's test for homogeneity of variances?

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Question 112

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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,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 .

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Question 113

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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 decision made implies that all 4 means are significantly different.

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,at a significance level of 1%,

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 11-11,what degrees of freedom should be used to determine the critical value of the F ratio against which to test for differences in the mean charges for doctors among the four primary specialty areas?

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,what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

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 decision made at 0.005 level of significance implies that all 3 means are significantly different.

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,

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?

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 null hypothesis for the F test for the block effects should be rejected at a 0.05 level of significance.