Direction: Please show work for non-multiple choice problems. posting your work TABLE 11-3 A realtor wants to compare the average 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. 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 Fill in blanks in the following table with the results of the analysis summarized in the following table: Source df Neighborhoods(among groups) Error(within groups) _______ Total SS ____ MS Show work below then answer questions followed after table completion. 1 F 1. Referring to Table 11-3, the among group degrees of freedom is a) 3 b) 4 c) 12 d) 16 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, degrees of freedom 2. Referring to Table 11-3, the within group sum of squares is a) 1.0606 b) 1.1825 c) 3.1819 d) 4.3644 ANSWER: 2 TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares 3. Referring to Table 11-3, the within group mean squares is a) 0.10 b) 0.29 c) 1.06 d) 1.18 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, mean squares 4. Referring to Table 11-3, a) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not all the same. b) at the 0.01 level of significance, the mean ratios for the 4 neighborhoods are all the same. c) at the 0.10 level of significance, the mean ratios for the 4 neighborhoods are not significantly different. d) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not significantly different from 0. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, decision, conclusion 5. Referring to Table 11-3, the null hypothesis for Levene's test for homogeneity of variances is a) H 0 : A B C D b) c) d) H0 : M A M B M C M D H 0 : A2 B2 C2 D2 H0 : A B C D ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene's test, form of hypothesis 3 TABLE 11-4 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: ANOVA Source of Variation Signs SS 14008.3 3 Starting Location 12288 Interaction Within 48 35305.3 3 Total 61649.6 7 df MS 14008.3 3 F P-value 0.11267 F crit 5.317645 2.78439 5 0.13374 5.317645 0.91950 5.31764 48 6 5 4413.16 7 11 6. Referring to Table 11-4, the degrees of freedom for the different building signs (factor A) is a) 1 b) 2 c) 3 d) 8 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, degrees of freedom 7. Referring to Table 11-4, the within (error) degrees of freedom is a) 1 b) 4 c) 8 d) 11 4 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, degrees of freedom 8. Referring to Table 11-4, the mean squares for starting location (factor B) is a) 48 b) 4,413.17 c) 12,288 d) 14,008.3 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, mean squares 9. Referring to Table 11-4, the F test statistic for testing the main effect of types of signs is a) 0.0109 b) 2.7844 c) 3.1742 d) 5.3176 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for factor 10. Referring to Table 11-4, the F test statistic for testing the interaction effect between the types of signs and the starting location is a) 0.0109 b) 2.7844 c) 3.1742 d) 5.3176 ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for interaction, interaction 11. Referring to Table 11-4, at 1% level of significance, a) there is insufficient evidence to conclude that the difference between the average traveling time for the different starting locations depends on the types of signs. b) there is insufficient evidence to conclude that the difference between the average traveling time for the different types of signs depends on the starting locations. 5 c) there is insufficient evidence to conclude that the relationship between traveling time and the types of signs depends on the starting locations. d) All of the above. ANSWER: TYPE: MC DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for factor, F test for interaction, decision, conclusion TABLE 11-9 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. SHAPES Circle Square Diamond Red 54 44 34 36 46 48 COLORS Green Blue 67 36 61 44 56 36 58 30 60 34 60 38 Yellow 45 41 21 25 31 33 12. Use a TWO-WAY ANOVA ANALYSIS TO FIND THE OUTPUT COPY FROM EXCEL AND PASTE BELOW ANSWER. Answer: 6 13. Referring to Table 11-9, the critical value in the test for significant differences between shapes is ________. ANSWER: TYPE: FI DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for factor, critical value 14. Referring to Table 11-9, the value of the statistic used to test for significant differences between shapes is ________. 7 ANSWER: TYPE: FI DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for factor, test statistic 15. True or False: Referring to Table 11-9, based on the results of the hypothesis test, it appears that there is a significant effect associated with the shape of the logo. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for factor, decision, conclusion 16. Referring to Table 11-9, the critical value in the test for a significant interaction is ________. ANSWER: TYPE: FI DIFFICULTY: Easy KEYWORDS: two-factor analysis of variance, F test for interaction, critical value 8