A consumer organization studied the effect of age of automobile owner on size of cash offer for a used car by utilizing 30 persons in three age groups (young, middle, elderly) who acted as the owner of a used car. A medium price, six-year-old car was selected for the experiment, and the "owners" solicited cash offers for this car from 30 dealers selected at random from the dealers in the region. The offers (in hundred dollars) were stored in the dataset (CashOffer.xlsx). (a) For a test about a difference in the mean amount of the offers among the age groups, fill in all the values in the following One-way ANOVA summary table. Source of Variation SS df MS F Among Groups ? ? ? ? Within Groups ? ? ? Total ? ? (b) At the 0.05 level of significance, is there evidence of a difference in the mean amount of the offers among the age groups? Test the hypothesis using one-way ANOVA. (c) At the 0.05 level of significance, determine which pair of age groups appear to differ significantly in the mean amount of the offers using the Tukey-Kramer method. (d) At the 0.05 level of significance, is there evidence of a difference in the variance of the offers among the age groups? Test the homogeneity of the variances using the Levene's test.
A partial result of the computation for a two-factor factorial experiment is given as follows. Source of Variation SS df MS F A 40 ? 20 ? B 210 ? ? 11.20 AB ? 6 15 ? Error ? 24 ? Total ? ? (a) Fill in all the missing results in the ANOVA table. (b) At the 0.10 level of significance, is there an interaction effect? Explain in the critical value approach. (c) At the 0.10 level of significance, is there evidence of an effect due to factor A? (d) At the 0.10 level of significance, is there evidence of an effect due to factor B?
. The marketing manager of a company producing a new cereal aimed for children wants to xamine the effect of the color and shape of the box's logo on the approval rating of the cereal. He ombined 4 colors and 2 shapes to produce a total of 8 designs. Each logo was presented to 3 lifferent groups (a total of 24 groups) and the approval rating for each was recorded and is stored LogoDesign.xlsx). The manager analyzed these data using the a = 0.05 level of significance for 11 inferences. (a) Here is the plot of means. What is the meaning of the blue and red lines cross each other? 80 60 40 20 0 Red Blue Yellow Green -Circle -Square (b) Is there a significant interaction between the color and shape of the logo? Explain in the p- value approach. (c) Is there a significant effect associated with the color of the logo? (d) Is there a significant effect associated with the shape of the logo?
Shape Circle Circle Circle Square Square Square Color Red 54.0 59.0 51.0 42.0 46.0 43.0 Blue 67.0 71.0 68.0 40.0 35.0 39.0 Yellow 50 47 51 34 38 Green 41 41 38 47 48 37 41
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