In marketing children's products, it is extremely important to produce television commercials that hold the attention of the children who view them. A psychologist hired by a marketing research firm wants to determine whether differences in attention span exist among advertisements for different types of products. A number of children under 10 years of age are asked to watch one 60-second commercial for one of three types of products, and their attention spans are measured in seconds. The results are shown in the accompanying table: Type of Product Advertised Toys/Games Children's Clothing Food/Candy 42 45 58 48 40 50 52355 30 35 42 60 32 57 38 a). At 5% level of significance, is there sufficient evidence to conclude that there are differences in the actual average attention span among the three types of product advertised? Show all necessary work. b). What type of error is possible and describe this error in terms of the problem. c). Explain the significance of the Tukey's analysis and how it works. Explain all aspects of the analysis very carefully. d). At 5% level of significance, use the Tukey's multiple comparison method to determine which types of product differ in terms of the actual average attention span. e). Using Minitab, generate the printouts of the plots for the statistical analysis you used in part (a). What information does each plot provide in terms of the above study? Explain Carefully.