3.00 points A telemarketing firm has studied the effects of two factors on the r
ID: 2946857 • Letter: 3
Question
3.00 points 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 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 cutput in table below The Telemarketing Data and the Excel Output of a Two-Way ANOVA Position of Advertisement Time of Day 10:00 maming On the Hour On the Hall-Hour Late in Program 60 47 47 38 64 4:00 aftemoon 61 56 79 127 123 128 9:00 evening 102 106 105 102 103 ANOVA: Two-Factor With Replication Summary Hour Half-Hour EarlyLateTotal 115 38.33 191 63.67 146 37.00 13.00 48.67 46.92 8.33 132.08 181 195 65.00 60.33 59.00 83.33 68.92 16.00 113.90 2.33 19.00 99.87 4.33 97.67 21.33 1,283 126.00 104.33 106.92 4.33 145.54 7.00 581 64.56 728.11 720.78 654 72.67 771.50 621.25 819 91.00 66.11Explanation / Answer
Result:
MINITAB used.
a).
Test for interaction, F=0.84, P=0.552, interaction is not significant.
b).
Test for time, F=976.27, P=0.000, Reject the null hypothesis.
c).
Test for position, F=115.46, P=0.000, Reject the null hypothesis).
d).
Difference
of Time
Levels
Simultaneous
95% CI
A-B
( -23.45, -16.55)
A-C
( -63.45, -56.55)
B-C
(-43.45,-36.55)
MINITAB RESULT
Tukey Simultaneous Tests for Differences of Means
Difference
of Time
Levels
Difference
of Means
SE of
Difference
Simultaneous
95% CI
T-Value
Adjusted
P-Value
B - A
20.00
1.38
(16.55, 23.45)
14.46
0.000
C - A
60.00
1.38
(56.55, 63.45)
43.39
0.000
C - B
40.00
1.38
(36.55, 43.45)
28.93
0.000
Individual confidence level = 98.02%
e).
Tukey Simultaneous Tests for Differences of Means
Difference
of Position
Levels
Simultaneous
95% CI
T-Value
Adjusted
P-Value
1-2
( -2.85,5.96)
-0.97
0.765
1-3
( -29.29,-20.49)
15.59
0.000
1-4
( -10.96, -2.15)
4.11
0.002
2-3
( -30.85,-22.04)
16.56
0.000
2-4
( -12.51,-3.71)
5.08
0.000
3-4
( 13.93, 22.74)
-11.48
0.000
MINITAB RESULT
Difference
of Position
Levels
Difference
of Means
SE of
Difference
Simultaneous
95% CI
T-Value
Adjusted
P-Value
2 - 1
-1.56
1.60
(-5.96, 2.85)
-0.97
0.765
3 - 1
24.89
1.60
(20.49, 29.29)
15.59
0.000
4 - 1
6.56
1.60
(2.15, 10.96)
4.11
0.002
3 - 2
26.44
1.60
(22.04, 30.85)
16.56
0.000
4 - 2
8.11
1.60
(3.71, 12.51)
5.08
0.000
4 - 3
-18.33
1.60
(-22.74, -13.93)
-11.48
0.000
Individual confidence level = 98.90%
f).
Position 2, Time A
Mean 37.0,
95% CI = (28.04, 45.96)
MINITAB RESULT
General Linear Model: calls versus Position, Time
Method
Factor coding
(-1, 0, +1)
Factor Information
Factor
Type
Levels
Values
Position
Fixed
4
1, 2, 3, 4
Time
Fixed
3
A, B, C
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Position
3
3973.6
1324.5
115.46
0.000
Time
2
22400.0
11200.0
976.27
0.000
Position*Time
6
57.8
9.6
0.84
0.552
Error
24
275.3
11.5
Total
35
26706.8
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
3.38707
98.97%
98.50%
97.68%
Difference
of Time
Levels
Simultaneous
95% CI
A-B
( -23.45, -16.55)
A-C
( -63.45, -56.55)
B-C
(-43.45,-36.55)
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