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1 a) Suppose that a symphony orchestra has tried three approaches, A, B, and C, to solicit funds from 30 generous local sponsors, 10sponsors per approach. The dollar amounts of the donations that resulted are in Table2EX.15. The column means are listed in the bottom row. For convenience when we revisit this example at the end of the next chapter, we rank-order the results in each column in descending order in presenting the table. Use an F test at  .05 to determine whether there are differences in amount of charitable donations due to solicitation approach. b) Consider the Table 3EX.2 data, which represent the amount of life insurance (in$1000s) for a random selection of seven state senators from each of three states:California, Kansas, and Connecticut. All of the senators are male, married, with two or three children, and between the ages of 40and 45. Because it appears that there could be major differences in variability from column to column, it was decided that a Kruskal-Wallis test would be performed to inquire whether amounts of life insurance differed by state/part of the country, at least with respect to state senators with these demographics. Conduct this test at  .05. 2 Consider the data in Table 4EX.10,which represents the amount of life insurance (in $1000s) carried by a random selection of seven state senators from each of three states: California, Kansas, and Connecticut. Perform Fisher’s LSD test for all three pairwise comparisons. 3. For Table 4EX.10, perform Tukey’s HSD test for all three pairwise comparisons. Use an experiment wise error rate of a = .05. 4. For Table 4EX.14a, perform a Dunnett’s test with column 3 as the control column. Use a = .05. 5. 2. This exercise is designed partly to illustrate that you often can’t tell what is going on just by looking at the data. Table 6EX.2 contains two sets of data—each has the same row means, column means, row SSQ, column SSQ, degrees of freedom, and about the same range of numbers a. For each set of data, perform an ANOVA, with alpha .05. The model is yij =  + I + j + ij b. Why are the results so dramatically different from one set to the other? c) For the exercise 2, set 1 data, perform Tukey’s HSD analysis on the column factor. Use an experiment wise error rate, a = .05. 6. For the exercise 2, set 1 data, perform a Newman-Keuls analysis on the column factor. Use an experimentwise error rate, a " .05. 7. a) Consider the Latin-square design in Table8EX.2 in which the row-factor levels represent different magazines, the column-factor levels represent different sizes of print advertisements, and the inside-factor levels represent different times of the year. The dependent variable is “number of orders generated from the advertisement.” Other factors inherent in the ad—positioning, location in the magazine and so on—are held constant. Analyze the experiment to determine if there are significant differences among magazines, among the different sizes of the advertisements, and among different times of the year. Use alpha .05. Note that we have used the “Latin-letters-on-the-inside” notation for the first time, to enhance the sense of the history of the field of experimental design. We also use old-style notation in Table 8EX.12. b) Suppose that in exercise 2 there had been a fourth factor (second inside factor), representing four different prices, thus forming a Graeco-Latin square, as shown in Table8EX.12. Analyze the data as a Graeco-Latin square, using alpha " .05. c) How many 3-level Graeco-Latin Squares are possible? {A “different” Graeco-Latin Square in this case is one that does not have the same exact set of 9 treatment combinations as another set of 9.} Provide proof (or, at least “support”) for your answer. 8) Suppose we wish to perform a one-way ANOVA, and that the four columns represent Brands A, B, C, and D, and the data values represent battery lifetimes. However, instead of having the individual data values, we have only the following information (referred to, often, as “summary statistics” – it is not unusual to receive data in this form.) BRAND A B C D Column Mean 38 28 32 34 Column Standard Deviation 6 5 7 9 Number of Data Points in Column 9 9 9 9 Provide the ANOVA table and test for the significance of BRAND. Use  = .05. 9) Consider the data below with three factors: A, B, and C; each factor has 2 levels. The data include three replicates at each of 8 treatment combinations of A, B, and C. And, suppose that we have the statistical model below, in which the level of A is indexed by i, the level of B is indexed by j, and the level of C is indexed by k, and “I” [of course] stands for interaction: Yijkl =  + i + j + k + Iij + Ijk + ijkl Provide the (copy and pasted) SPSS ANOVA table your analysis is based on, and determine the impact/significance of all the sources of variability (except, of course, for “error”). Use  = .05. 10) Suppose that we have an experiment in which we are studying the dependent variable of “time to perform a task.” There are two factors; one factor is the AGE (Younger, Older) of the person performing the task, and the other factor is the SEX (Male, Female) of the person performing the task. For each of the statements below, does the the statement signify that there is no interaction between AGE and SEX. a) The difference in average performance time between Males and Females (Male minus Female), plus the difference in average performance time between Younger people and Older people (Younger minus Older) equals the difference in average performance time between Younger Males and Older Females. YES____ NO____ b) The difference in average performance time between Males and Females is the same for people of different ages. YES____ NO____ c) The difference in average performance time between Younger People and Older People is the same as the difference in average performance time between Males and Females. YES____ NO____ d) The AGE effect on average performance time is the same as the SEX effect on average performance time. YES____ NO____ e) The difference in average performance time between Younger people and Older people is different for Males and Females. YES____ NO____

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