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A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table. Bottle Design Study Data A с 16 19 16 18 16 SUMMARY Groups Design A B 35 33 35 33 30 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. Design B Design C 26 20 25 21 26 Count Sum Average Variance 85 17.0 2.0 166 33.2 4.2 118 23.6 8.3 5 5 5 ANOVA Source of Variation Between Groups Within Groups Total Point estimate Confidence interval μB -μA: μC -μA: |ỤC –UB: SS 663.6000 58.0 721.6000 ,[ ,[ ,[ df 2 12.0 14 MS 331.8000 4.8330 F 68.65 P-Value 2.70E-07 (b) Consider the pairwise differences μB - HA, HC - HA, and μc - HB. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) F crit 3.88529

A consumer preference study compares the effects of three different bottle designs (A, B, and C) on sales of a popular fabric softener. A completely randomized design is employed. Specifically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table. Bottle Design Study Data A с 16 19 16 18 16 SUMMARY Groups Design A B 35 33 35 33 30 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. Design B Design C 26 20 25 21 26 Count Sum Average Variance 85 17.0 2.0 166 33.2 4.2 118 23.6 8.3 5 5 5 ANOVA Source of Variation Between Groups Within Groups Total Point estimate Confidence interval μB -μA: μC -μA: |ỤC –UB: SS 663.6000 58.0 721.6000 ,[ ,[ ,[ df 2 12.0 14 MS 331.8000 4.8330 F 68.65 P-Value 2.70E-07 (b) Consider the pairwise differences μB - HA, HC - HA, and μc - HB. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) F crit 3.88529

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Consumer Preference Study on Bottle Designs** A study was conducted to compare the effects of three different bottle designs (A, B, and C) on the sales of a popular fabric softener. A completely randomized design was used, selecting 15 supermarkets of equal sales potential, with 5 supermarkets assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is shown below: **Bottle Design Study Data:** - **Design A:** 16, 19, 16, 18, 16 - **Design B:** 35, 33, 35, 33, 30 - **Design C:** 26, 20, 25, 21, 26 **ANOVA Results:** A one-way ANOVA was performed to analyze the data. The Excel output is shown below: **Summary Table:** - **Design A:** Count: 5, Sum: 85, Average: 17.0, Variance: 2.0 - **Design B:** Count: 5, Sum: 166, Average: 33.2, Variance: 4.2 - **Design C:** Count: 5, Sum: 118, Average: 23.6, Variance: 8.3 **ANOVA Table:** - **Source of Variation:** Between Groups, Within Groups, Total - **SS (Sum of Squares):** Between: 663.6000, Within: 58.0, Total: 721.6000 - **df (Degrees of Freedom):** Between: 2, Within: 12 - **MS (Mean Square):** Between: 331.8000, Within: 4.8330 - **F-Value:** 68.65 - **P-Value:** 2.70E-07 - **F crit:** 3.88529 **Pairwise Differences Analysis:** (b) Calculate the pairwise differences \((\mu_B - \mu_A), (\mu_C - \mu_A), \text{ and } (\mu_C - \mu_B)\). Also, find the point estimate and a Tukey simultaneous 95% confidence interval for each pairwise difference. Interpret the results to determine which bottle design maximizes mean daily sales. (Round answers to two decimal places, with negative amounts indicated by a minus sign.) **Point
Transcribed Image Text:**Consumer Preference Study on Bottle Designs** A study was conducted to compare the effects of three different bottle designs (A, B, and C) on the sales of a popular fabric softener. A completely randomized design was used, selecting 15 supermarkets of equal sales potential, with 5 supermarkets assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is shown below: **Bottle Design Study Data:** - **Design A:** 16, 19, 16, 18, 16 - **Design B:** 35, 33, 35, 33, 30 - **Design C:** 26, 20, 25, 21, 26 **ANOVA Results:** A one-way ANOVA was performed to analyze the data. The Excel output is shown below: **Summary Table:** - **Design A:** Count: 5, Sum: 85, Average: 17.0, Variance: 2.0 - **Design B:** Count: 5, Sum: 166, Average: 33.2, Variance: 4.2 - **Design C:** Count: 5, Sum: 118, Average: 23.6, Variance: 8.3 **ANOVA Table:** - **Source of Variation:** Between Groups, Within Groups, Total - **SS (Sum of Squares):** Between: 663.6000, Within: 58.0, Total: 721.6000 - **df (Degrees of Freedom):** Between: 2, Within: 12 - **MS (Mean Square):** Between: 331.8000, Within: 4.8330 - **F-Value:** 68.65 - **P-Value:** 2.70E-07 - **F crit:** 3.88529 **Pairwise Differences Analysis:** (b) Calculate the pairwise differences \((\mu_B - \mu_A), (\mu_C - \mu_A), \text{ and } (\mu_C - \mu_B)\). Also, find the point estimate and a Tukey simultaneous 95% confidence interval for each pairwise difference. Interpret the results to determine which bottle design maximizes mean daily sales. (Round answers to two decimal places, with negative amounts indicated by a minus sign.) **Point
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