Exam 11: Analysis of 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 p-value of the test statistic for the randomized block F test for the difference in the means?

In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may

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 should be the conclusion for the Levene's test for homogeneity of variances at a 5% 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 decision made implies that all 4 means are significantly different.

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, using an overall level of significance of 0.01, the critical value of the Studentized range used in calculating the critical range for the Tukey-Kramer procedure 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, interpret the test for interaction.

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 in the test for a significant interaction is ________.

In a one-way ANOVA, the null hypothesis is always

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

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 are the degrees of freedom of the F test statistic for testing the block effects?

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 are the degrees of freedom of the Studentized range distribution for the Tukey multiple comparison procedure?

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, using an overall level of significance of 0.01, what is the critical range for the Tukey multiple comparison procedure?

SCENARIO 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 Scenario 11-9, at the 0.01 level, what conclusions can you reach from the analysis?

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 amount of total variation or SST 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 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.

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 decision made at a 0.05 level of significance on the F test for the block effects implies that the blocking has been advantageous in reducing the experiment error.

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, based on the results of the hypothesis test, it appears that there is a significant effect on the approval rating associated with the color of the logo.

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 numerator and denominator degrees of freedom of the test ratio are ________ and ________, respectively.

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 decision made at a 0.01 level of significance on the randomized block F test for the difference in means implies that all 3 means are significantly different.

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 total variation or SST is ________.