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Exam 11: Analysis of Variance

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Question 51

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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, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is a significant difference between all pairs of mean speeds.

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B) False

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Question 52

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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 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 Smith and Walsh seeds.

A) True
B) False

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Question 53

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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 within group sum of squares 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 value of the F test statistic for testing the block effects?

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 p-value of the test statistic for Levene's test for homogeneity of variances?

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 relative efficiency means that 15.23 times as many observations in each brand would be needed in a one-way ANOVA design as compared to the randomized block design in order to obtain the same precision for comparison of the different means.

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 critical value of the test for significant differences between colors 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 among-group variation or SSA is __________.

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

The F test statistic in a one-way ANOVA is

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

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 within-group variation or SSW is __________.

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,

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.

The MSE must always be positive.

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

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 11-7 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 estimated relative efficiency?

Interaction in an experimental design can be tested in

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 the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.