Exam 11: Analysis of Variance

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 null hypothesis for testing the block effects?

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, the among-group (between-group)mean squares 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-group variation or SSA is __________.

Analysis of variance designs use samples that represent each group and subdivides the total variation to determine possible differences among the variances of each group.

When the F test is used for ANOVA, the rejection region is always in the right tail.

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 critical value for testing the block effects at a 0.05 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, 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 __________.

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 are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

SCENARIO 11-11 A physician and president of a Tampa Health Maintenance Organization (HMO)are attempting to show the benefits of managed health care to an insurance company.The physician believes that certain types of doctors are more cost-effective than others.One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians.To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP)- and recorded the total charges per member per month for each.A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate.The president theorizes that foreign graduates will have higher mean charges than USA graduates.To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above.So, information on charges for 40 doctors (20 foreign and 20 USA medical school graduates)was obtained for each of the 4 specialties.The results for the ANOVA are summarized in the following table. -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 between the mean charges of foreign and USA medical school graduates?

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 are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

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 the fewest mean number of 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 given below.How should the data be analyzed?

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 sporting goods retailer decided to perform an ANOVA F test.The amount of total variation or SST 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, 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.

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

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-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 11-1 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, the total degrees of freedom 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, 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.

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

An interaction between factors A and B in a factorial analysis occurs when the effect of factor A is different for various levels of factor B.

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 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.