Exam 11: Analysis of Variance

A completely randomized design

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, if a level of significance of 0.05 is chosen, the null hypothesis should be rejected.

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, the among-group variation or SSA is _________.

The analysis of variance (ANOVA)tests hypotheses about the population variance.

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 upper-tail critical value of the Studentized range distribution for the Tukey multiple comparison procedure at the 5% level of significance?

Which of the following is true regarding ANOVA?

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 mean square for the factor color is ________.

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 within group variation or SSW is __________.

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 mean square for the factor shape is ________.

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 interaction between the two factors?

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 decision for the Levene's test for homogeneity of variances at a 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.

A completely randomized design with 4 groups would have 6 possible pairwise comparisons.

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, if a level of significance of 0.05 is chosen, the decision made indicates that at least 2 of the 5 locations have different mean occupancy rates.

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, using an overall level of significance of 0.05, the critical range for the Tukey-Kramer procedure is ________.

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 11-5 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, the null hypothesis for Levene's test for homogeneity of variances 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 value of MSA is __________, while MSW is __________.

In a two-factor ANOVA analysis, the sum of squares due to both factors, the interaction sum of squares and the within sum of squares must add up to the total sum of squares.

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 randomized block F test is valid only if the population of crop yields is normally distributed for the 3 varieties.