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
42
36
62
51
37
41
68
47
41
38
64
48
4:00 afternoon
62
57
88
67
60
60
85
60
58
55
81
66
9:00 evening
100
97
127
105
96
96
120
101
103
101
126
107
ANOVA: Two-Factor With Replication
Summary
Hour
Half-Hour
Early
Late
Total
Morning
Count
3
3
3
3
12
Sum
120
115
194
146
575
Average
40
38.33
64.67
48.67
47.92
Variance
7
6.33
9.33
4.33
123.72
Afternoon
Count
3
3
3
3
12
Sum
180
172
254
193
799
Average
60
57.33
84.67
64.33
66.58
Variance
4
6.33
12.33
14.33
132.45
Evening
Count
3
3
3
3
12
Sum
299
294
373
313
1279
Average
99.67
98
124.33
104.33
106.58
Variance
12.33
7
14.33
9.33
128.27
Total
Count
9
9
9
9
Sum
599
581
821
652
Average
66.56
64.56
91.22
72.44
Variance
697.53
701.78
700.69
625.03
ANOVA
Source of Variation
SS
df
MS
F
P-Value
F crit
Sample
21560.89
2
10780.444
1209.02
8.12E-25
3.403
Columns
3989.42
3
1329.806
149.14
1.19E-15
3.009
Interaction
25.33
6
4.222
0.47
0.8212
2.508
Error
214
24
8.917
Total
25789.64
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
q.05=3.53 MSE 8.917
(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.)
(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.)