A large advertising firm specializes in creating television commercials for children€™s products. The firm wants to design a study to investigate factors that may affect the lengths of time a commercial is able to hold a child€™s attention. A preliminary study determines that two factors that may be important are the age of the child and the type of product being advertised. The firm wants to determine whether there were large differences in the mean length of time that the commercial is able to hold the child€™s attention depending on these two factors. If there proves to be a difference, the firm would then attempt to determine new types of commercials depending on the product and targeted age group. Three age groups are used:
A1: 5€“ 6 years A2: 7€“ 8 years A3: 9€“ 10 years
The types of products selected are
P1: breakfast cereals P2: video games
A group of 30 children is recruited in each age group, and 10 are randomly assigned to watch a 60-second commercial for each of the two products. Researchers record their attention spans during the viewing of the commercial. The data are given here.

a. Identify the design.
b. Write a model for this situation, identifying all the terms in the model.
c. Estimate the parameters in the model.
d. Compute the sum of squares for the data, and summarize the information in an AOV table.

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51 52 43 48 39 33 56 43 40 51 45 A-30 47 6 2 4 6 3 4 3 25 767,4 16 3.8 .4 2423422 9822626376 1,1 31321 A-37 6 28 4 32 16 8 41 29 18 210 ,-3684 32 16 8 4 2 19 35 22 28 95 22 2 1 2 2 1 3 81 27 27 16 3 8 196 、 19 36 40 30 4 10 30 5 34 21 22, 1234567890 Mean by age group: A A AMean by product type: Pi P 23.0 25,05 33.75 2147 33.07