Answered: 16. In an experiment, you measure the…

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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Transcribed Image Text:**Title: Analyzing the Effect of Gender and Brand on Soft Drink Popularity** In an experiment, the popularity of two brands of soft drinks (Factor A) was measured, with each brand tested among males and females (Factor B). The following table shows the main effect and cell means from the study: | | Factor A | |-------------------|----------| | | Level A₁: Brand X | Level A₂: Brand Y | | Factor B | | | | Level B₁: Males | 14 | 23 | | Level B₂: Females | 25 | 12 | **Questions:** (a) Describe the graph of the interaction when Factor A is on the X-axis. (b) Does there appear to be an interaction effect? Why? (c) What are the main effect means and thus the main effect of changing brands? (d) What are the main effect means and thus the main effect of changing gender? (e) Why will a significant interaction prohibit you from making conclusions based on the main effects? **Analysis of Data:** - When plotting the data with Factor A on the X-axis (Brand X versus Brand Y), the interaction graph will show two lines, one for each gender. - For Males: Popularity is higher for Brand Y (23) compared to Brand X (14). - For Females: Popularity is higher for Brand X (25) compared to Brand Y (12). - **Interaction Effect:** The differing direction of popularity between brands for males and females indicates a potential interaction effect, suggesting that the preference for the soft drink brand depends on the gender. - **Main Effect of Brand:** To assess the main effect of changing brands, average the popularity scores across genders for each brand: - Brand X: (14 + 25)/2 = 19.5 - Brand Y: (23 + 12)/2 = 17.5 This suggests that, on average, Brand X is slightly more popular. - **Main Effect of Gender:** To assess the main effect of changing gender, average the popularity scores across brands for each gender: - Males: (14 + 23)/2 = 18.5 - Females: (25 + 12)/2 = 18.5 The average popularity is the same for both males and females. - **Significant Interaction

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