Answered: Data was collected on ratings of two…

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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Data was collected on ratings of two brands of coffee on four characteristics: taste, aroma, richness, and acidity. The distribution is unknown, but symmetric. Is there evidence of a difference in the median ratings between the two brands? Use a Wilcoxen Matched-Pairs Signed Rank Test to answer this question at a 5% significance level. Differences = Brand A - Brand B.

Brand A    Brand B
24            26
27            27
19            22
24            27
22            25
26            27
27            26
25            27
22            23

What is the value of T?

What is the critical value?

At a 5% significance level, what can you conclude from this study?

(a) There is no significant difference in the median ratings between the two coffee brands.

(b) Brand A is rated significantly lower than Brand B.

(c)There is a significant difference in the median ratings between the two coffee brands.

(d) Brand A is rated significantly higher than Brand B.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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