Answered: Nine experts rated two brands of coffee…

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:The image displays a data table comparing scores given by different experts to two brands, labeled Brand A and Brand B. Here's the transcription of the table: **Data Table** | Expert | Brand A | Brand B | |--------|---------|---------| | C.C. | 24 | 25 | | S.E. | 25 | 25 | | E.G. | 19 | 21 | | B.I. | 22 | 24 | | C.M. | 22 | 24 | | C.N. | 24 | 25 | | G.N. | 27 | 26 | | R.M. | 21 | 22 | | P.V. | 22 | 23 | The table organizes data by listing experts in the first column, along with their respective scores for Brand A and Brand B in the subsequent columns. This setup allows for an easy comparison of how each expert rated the two brands.

$**Educational Webpage Content:** **Title: Statistical Analysis of Coffee Taste-Testing Experiment** **Introduction:** In a scientific taste-testing experiment, nine experts evaluated two different brands of coffee. Each coffee was rated on a 7-point scale across four characteristics: taste, aroma, richness, and acidity. A score of 1 indicates an extremely unpleasing experience, while a score of 7 signifies an extremely pleasing one. The cumulative scores from all four characteristics for each brand were tabulated for analysis. **Objective:** To determine if there is a significant difference in mean ratings between the two coffee brands at a 0.01 level of significance. **Methodology:** Let $\mu_1$ represent the mean rating for brand A and $\mu_2$ represent the mean rating for brand B. The task is to establish the null ($H_0$) and alternative ($H_1$) hypotheses to examine any differences in mean ratings. **Hypotheses Options:** - **Option A:** - Null Hypothesis ($H_0$): $\mu_D = 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D \neq 0$ - **Option B:** - Null Hypothesis ($H_0$): $\mu_D \geq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D < 0$ - **Option C:** - Null Hypothesis ($H_0$): $\mu_D \neq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D = 0$ - **Option D:** - Null Hypothesis ($H_0$): $\mu_D \leq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D > 0$ **Selected Hypothesis:** Option A is chosen as the correct formulation: - **Null Hypothesis (\($

Transcribed Image Text:**Educational Webpage Content:** **Title: Statistical Analysis of Coffee Taste-Testing Experiment** **Introduction:** In a scientific taste-testing experiment, nine experts evaluated two different brands of coffee. Each coffee was rated on a 7-point scale across four characteristics: taste, aroma, richness, and acidity. A score of 1 indicates an extremely unpleasing experience, while a score of 7 signifies an extremely pleasing one. The cumulative scores from all four characteristics for each brand were tabulated for analysis. **Objective:** To determine if there is a significant difference in mean ratings between the two coffee brands at a 0.01 level of significance. **Methodology:** Let $\mu_1$ represent the mean rating for brand A and $\mu_2$ represent the mean rating for brand B. The task is to establish the null ($H_0$) and alternative ($H_1$) hypotheses to examine any differences in mean ratings. **Hypotheses Options:** - **Option A:** - Null Hypothesis ($H_0$): $\mu_D = 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D \neq 0$ - **Option B:** - Null Hypothesis ($H_0$): $\mu_D \geq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D < 0$ - **Option C:** - Null Hypothesis ($H_0$): $\mu_D \neq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D = 0$ - **Option D:** - Null Hypothesis ($H_0$): $\mu_D \leq 0$ (where $\mu_D = \mu_1 - \mu_2$) - Alternative Hypothesis ($H_1$): $\mu_D > 0$ **Selected Hypothesis:** Option A is chosen as the correct formulation: - **Null Hypothesis (\(

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