Exam 11: Analysis of Variance

Instruction 11-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She recorded three trials of each brand and determined their maximum downhill speeds. The results are presented in kilometres per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-3,the null hypothesis should be rejected at a 5% level of significance.

Instruction 11-9 A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below: ANONA Source of Vartation SS df MS F \rho -value F crit Signs 14008.33 14008.33 0.11267 5.317645 Starting Location 12288 2.784395 0.13374 5.317645 -Referring to Instruction 11-9,at 1% level of significance,

Instruction 11-2 A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A, B, C, and D). Four properties are randomly selected from each neighbourhood 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 summarised in the following table: Source df SS MS F PR > F Neighbbourhoods 3.1819 1.0606 10.76 0.001 Error 12 Total -Referring to Instruction 11-2,the within group mean squares is

Different populations used in analysis of variance are known as groups.

Instruction 11-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomised design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-7,using an overall level of significance of 0.01,what is the critical range for the Tukey multiple comparison procedure?

Instruction 11-11 An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants all three varieties of the seeds on each of five different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomised block design, the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-11,the decision made at a 0.005 level of significance implies that all three means are significantly different.

Instruction 11-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomised design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-7,the among-group variation or SSA is________.

When would you use the Tukey-Kramer procedure?

Instruction 11-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomised design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-7,the null hypothesis for the randomised block F test for the difference in the means is

Instruction 11-8 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 a 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 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 * 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. Source df S5 MS F PR > F Subjectvisibility 1 1380.24 1380.24 4.26 0.043 Test taker success 1 1325.16 1325.16 4.09 0.050 Interaction 1 3385.80 3385.80 10.45 0.002 Error 36 11,664.00 324.00 Total 39 17.755.20 -Referring to Instruction 11-8,at the 0.01 level,what conclusions can you draw from the analyses?

Instruction 11-4 A hotel chain has identically sized resorts in five locations. The following data resulted from analysing the hotel guests on randomly selected days in the five locations. ROW Caymen Pennkapmp California Mayaguez Maui 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Analysis of Variance }$ Analysis of Variancs Source d f SS MS F p Location 4 11.47 0.001 Error 10 Total -Referring to Instruction 11-4,the value of MSA is ________ while MSW is ________.

In a two-way ANOVA the degrees of freedom for the interaction term is

Instruction 11-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She recorded three trials of each brand and determined their maximum downhill speeds. The results are presented in kilometres per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-3,construct the ANOVA table from the sample data.

Instruction 11-9 A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below: ANONA Source of Vartation SS df MS F \rho -value F crit Signs 14008.33 14008.33 0.11267 5.317645 Starting Location 12288 2.784395 0.13374 5.317645 -Referring to Instruction 11-9,the F test statistic for testing the interaction effect between the types of signs and the starting location is

Instruction 11-4 A hotel chain has identically sized resorts in five locations. The following data resulted from analysing the hotel guests on randomly selected days in the five locations. ROW Caymen Pennkapmp California Mayaguez Maui 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Analysis of Variance }$ Analysis of Variancs Source d f SS MS F p Location 4 11.47 0.001 Error 10 Total -Referring to Instruction 11-4,what is the value of the test statistic for Levene's test for homogeneity of variances?

Instruction 11-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She recorded three trials of each brand and determined their maximum downhill speeds. The results are presented in kilometres per hour in the table below. Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Instruction 11-3,the value of MSA is _____,while MSW is ___________.

Instruction 11-9 A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below: ANONA Source of Vartation SS df MS F \rho -value F crit Signs 14008.33 14008.33 0.11267 5.317645 Starting Location 12288 2.784395 0.13374 5.317645 -Referring to Instruction 11-9,the mean squares for starting location (factor is

The MSE must always be positive.

Instruction 11-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds. She plants 15 fields, five with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomised design, the results are presented in the table that follows. Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 -Referring to Instruction 11-6,the value of MSA is ______,while MSW is ________.

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