A study was conducted by a television network in a certain state to evaluate the viewing characteristics of adult females. Each individual in a stratified random sample of 480 women was sent a questionnaire; the strata were formed on the basis of the following three factors: season (winter or summer), region (eastern, central, or western), and residence (rural or urban). The averages of the total time reported watching TV (hours per day) are summarized in the accompanying table of sample means and standard deviations.

a. Suppose that the questionnaire contained items concerning additional factors such as occupation (categorized as housewife, blue-collar worker, white-collar worker, or professional), age (categorized as 20 to 34, 35 to 50, and over 50), and number of children (categorized as 0, 1 €“ 2, and 3+). What is the likelihood of obtaining equal cell numbers when carrying out an ANOVA to consider these additional variables?
b. Examine the table of sample means for main effects and interactions. (You may want to form two-factor summary tables for assessing two-factor interactions.)
c. Using the following table of ANOVA results, carry out appropriate F tests, and discuss your results.
d. State a regression model appropriate for obtaining information equivalent to the ANOVA results presented next.

Winter Marginals Summer Residence and Region Rural 1.340 1.380 4.80 4.85 4.78 0.851 0.935 0,843 3.78 3.80 3.71 3.76 40 Central West Marginals 2.75 2.65 2.72 80 80 80 240 40 120 Urban East Central 3.65 4.50 4.05 4.07 3.52 3.83 3.85 3.73 0.958 3.15 3.65 3.39 .947 0.743 0.781 80 80 240 0.779 40 Marginals 120 120 Marginals 240 240 4.44 480 3.75 Source d.f MS RESID REGION SEASON RESID X REGION RESID X SEASON REGION X SEASON RESIDX REGION X SEASON Error 0,1333 25527 229.63 3.3247 60.492 7.2247 6,7460 478.21 0.1333 1.2763 229,63 16623 60.492 3.6123 3.3730 1.0218 468