In a market research study, members of a consumer test panel are asked to rate the visual appeal (on a 1 to 10 scale) of the texture of dashboard plastic trim in a mockup of a new fuel cell car. The manufacturer is testing four finish textures. Panelists are assigned randomly to evaluate each texture. The test results are shown below. Each cell shows the average rating by panelists who evaluated each texture. Research question: Is mean rating affected by age group and/or by surface type? Mean Ratings of Dashboard Surface TextureAge GroupShinySatinPebbledPatternYouth (under 21)6.56.15.54.4Adult (21 to 39)5.35.96.55.7Middle-Age (40 to 61)4.65.16.85.2Senior (62 and over)3.44.76.24.6b) Fill in the missing data. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.) ANOVA TableSourcedfMSFp-valueRows (Age Group)Columns (Surface)ErrorTotal Table of MeansStandardMeannDeviationShiny4Satin4Pebbled4PatternYouth (Under 21)Adult (21 to 39)4Middle-Age (40 to 61)4Senior (62 and over)4Total4.4.

ANOVA is a statistical procedure that is utilized for testing the differences among the means of many populations. As the technique is related to regression, the independent variables will be qualitative whereas the dependent variables will be quantitative.

Answered: In a market research study, members of…

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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In a market research study, members of a consumer test panel are asked to rate the visual appeal (on a 1 to 10 scale) of the texture of dashboard plastic trim in a mockup of a new fuel cell car. The manufacturer is testing four finish textures. Panelists are assigned randomly to evaluate each texture. The test results are shown below. Each cell shows the average rating by panelists who evaluated each texture. Research question: Is mean rating affected by age group and/or by surface type?

Age Group	Shiny	Satin	Pebbled	Pattern
Mean Ratings of Dashboard Surface Texture
Youth (under 21)	6.5	6.1	5.5	4.4
Adult (21 to 39)	5.3	5.9	6.5	5.7
Middle-Age (40 to 61)	4.6	5.1	6.8	5.2
Senior (62 and over)	3.4	4.7	6.2	4.6

b) Fill in the missing data. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

ANOVA Table
Source
df
MS
F
p-value
Rows (Age Group)
Columns (Surface)
Error
Total

Table of Means
Standard
Mean
n
Deviation
Shiny
4
Satin
4
Pebbled
4
Pattern
Youth (Under 21)
Adult (21 to 39)
4
Middle-Age (40 to 61)
4
Senior (62 and over)
4
Total
4.
4.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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