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 the following table, 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 the table below. The Telemarketing Data and the Excel Output of a Two-Way ANOVA Position
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 the following table, 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 the table below.
| The Telemarketing Data and the Excel Output of a Two-Way ANOVA | ||||
| Position of Advertisement | ||||
| Time of Day | On the Hour | On the Half-Hour | Early in Program | Late in Program |
| 10:00 morning | 44 | 35 | 59 | 49 |
| 36 | 40 | 68 | 46 | |
| 40 | 36 | 66 | 49 | |
| 4:00 afternoon | 62 | 55 | 89 | 65 |
| 62 | 60 | 84 | 59 | |
| 59 | 53 | 80 | 64 | |
| 9:00 evening | 105 | 97 | 125 | 104 |
| 96 | 98 | 122 | 103 | |
| 105 | 104 | 129 | 110 | |
| ANOVA: Two-Factor With Replication | |||||
| Summary | Hour | Half-Hour | Early | Late | Total |
| Morning | |||||
| Count | 3 | 3 | 3 | 3 | 12 |
| Sum | 120 | 111 | 193 | 144 | 568 |
| Average | 40.00 | 37.00 | 64.33 | 48.00 | 47.33 |
| Variance | 16.00 | 7.00 | 22.33 | 3.00 | 131.52 |
| Afternoon | |||||
| Count | 3 | 3 | 3 | 3 | 12 |
| Sum | 183 | 168 | 253 | 188 | 792 |
| Average | 61.00 | 56.00 | 84.33 | 62.67 | 66.00 |
| Variance | 3.00 | 13.00 | 20.33 | 10.33 | 137.27 |
| Evening | |||||
| Count | 3 | 3 | 3 | 3 | 12 |
| Sum | 306 | 299 | 376 | 317 | 1,298 |
| Average | 102.00 | 99.67 | 125.33 | 105.67 | 108.17 |
| Variance | 27.00 | 14.33 | 12.33 | 14.33 | 124.52 |
| Total | |||||
| Count | 9 | 9 | 9 | 9 | |
| Sum | 609 | 578 | 822 | 649 | |
| Average | 67.67 | 64.22 | 91.33 | 72.11 | |
| Variance | 757.25 | 782.94 | 739.00 | 680.61 | |
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-Value | F crit |
| Sample | 23,308.67 | 2 | 11,654.33 | 857.99 | .0000 | 3.403 |
| Columns | 3,956.56 | 3 | 1,318.85 | 97.09 | .0000 | 3.009 |
| Interaction | 43.78 | 6 | 7.30 | .54 | .7747 | 2.508 |
| Error | 326.00 | 24 | 13.583 | |||
| Total | 27,635.00 | 35 | ||||
(d) Make pairwise comparisons of the morning, afternoon, and evening times by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
Tukey q0.05 = 3.53, MSE = 13.583
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(e) Make pairwise comparisons of the four ad positions by using Tukey simultaneous 95 percent confidence intervals. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)
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(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. (Round your answers to 2 decimal places.)
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