A telemarketing firm has studied the effects of two factors on the response to its television advertisements. The first factor is the time of day at which the ad is run, while the second is the position of the ad within the hour. The data in Table 11.16, which were obtained by using a completely randomized experimental design, give the number of calls placed to an 800 number following a sample broadcast of the advertisement. If we use Excel to analyze these data, we obtain the output in Figure 11.15.
TABLE 11.16
Results of a Two-Factor Telemarketing Response Experiment

FIGURE 11.15
Excel Output of a Two-Way ANOVA of the Telemarketing Data

a. Perform graphical analysis to check for interaction between time of day and position of advertisement. Explain your conclusion. Then test for interaction with α = .05.
b. Test the significance of time of day effects with α = .05.
c. Test the significance of position of advertisement effects with α = .05.
d. Make pairwise comparisons of the morning, afternoon, and evening times by using Tukey simultaneous 95 percent confidence intervals.
e. Make pairwise comparisons of the four ad positions by using Tukey simultaneous 95 percent confidence intervals.
f. Which time of day and advertisement position maximizes consumer response? Compute a 95 percent (individual) confidence interval for the mean number of calls placed for this time of day/ad position combination.

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Position of Advertisement Time of Day 10:00 morning On the Hour On the Half-Hour Early in Program Late in Program 42 37 36 38 57 60 62 68 64 51 47 48 67 60 4:00 afternoon 62 60 58 100 96 103 85 81 127 120 126 9:00 evening 97 96 101 105 101 107 ANOVA: Two-Factor With Replication Summary Hour Half-Hour Early ae Total Morning Count Sum Average Variance Afternoon Count 150 100 -Morning 12 575 38.3 64.7 48.7 47.9 6.3 9.3 43 23.7 Afternoon Evening 120 115 194 146 40 50 Hour Half-Hour Early Late 12 799 60 57.3 84.7 64.3 66.6 4 63 23 14.3 132.4 180 172 254 193 Average Variance Evening Count ANOVA Source of Variation 5S df MS F P-value F crit 12 299 294 373 313 1279 99.67 98 124.3 104.3 106.6 7 14.3 9.3 128.3 21560.89 210780.444 1209.0 8.12E-25 3.403 Average Variance 396942 31329806 14914 1.191509 119E-15 3.009 0.8212 2508 Columns Interaction Within Total 12.33 0.47 25.33 6 214 24 25789.64 35 4222 8.917 Total Count Sum Average 66.56 Variance 697.53 701.78 700.69 625.03 599 81 81 652 64.56 91.22 72.44