In a market research study, members of a consumer test panel are asked to rate t
ID: 2927099 • Letter: I
Question
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 Texture
(a-1) Which type of ANOVA model should be used?
(a-2) Choose the correct row-effect hypotheses.
(a-3) Choose the correct column-effect hypotheses.
(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.)
(c) Choose the correct statement.
Mean Ratings of Dashboard Surface Texture
Age Group Shiny Satin Pebbled Pattern Youth (under 21) 6.6 6.0 5.8 4.6 Adult (21 to 39) 5.1 5.4 6.3 5.0 Middle-Age (40 to 61) 4.1 5.9 6.2 5.9 Senior (62 and over) 3.0 4.3 6.9 4.5
Explanation / Answer
a-1 There are two factors-Factor A (age group) and Factor B(dashboard surface texture). Each factor has four levels. Note that for each age and dashboard surface texture combination, only 1 reading is available. This explains why two-factor without replication should be used.
a-2 Note, factor A has four levels, thus the number of main effect terms for factor A will be one less than number of levels of factor A. Equivalently, number of main effect terms for factor B will be one less than the number of levels of main factor B. The full model is as follows:
The null hypothesis for row factor is as follows:
H0: A1=A2=A3 versus H1:not all the Aj s are equal to zero.
a-3H0:B1-B2-B3 versus H1:not all Bk s are equal to zero.
b. Enter data in Excel-Data-Data Analysis-type B2:E5 in the Input range and check Output range and type G3. Click OK. The output is displayed.
The ANOVA table is as follows:
c. Per rejection rule based on p avlue, reject null hypothesis if p value i sless than alpha=0.05. Here, p values for neither row nor column is less than 0. Thus, conclude that texture is not significantly affected by age group or by surface type.
Mean n s Shiny 4.7 4 1.530 Satin 5.4 4 0.7789 Pebbled 6.3 4 0.4546 Pattern 5 4 0.6377 Total 21.4 16 3.4012 Youth 5.75 4 0.8386 Adult 5.45 4 0.5916 Middle-age 5.525 4 0.9605 Senior 4.675 4 1.6257 Total 21.4 16 4.0164Related Questions
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