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
muM - muA: [     ],[     ]
muM - muE: [     ],[     ]
muA - muE: [     ],[     ]

(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.)

mu1 - mu2: [     ],[     ]
mu1 - mu3: [     ],[     ]
mu1 - mu4: [     ],[     ]
mu2 - mu3: [     ],[     ]
mu2 - mu4: [     ],[     ]
mu3 - mu4: [     ],[     ]

(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.)

CI: [     ],[     ]

Question

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
muM - muA: [     ],[     ]
muM - muE: [     ],[     ]
muA - muE: [     ],[     ]

(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.)

mu1 - mu2: [     ],[     ]
mu1 - mu3: [     ],[     ]
mu1 - mu4: [     ],[     ]
mu2 - mu3: [     ],[     ]
mu2 - mu4: [     ],[     ]
mu3 - mu4: [     ],[     ]

(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.)

CI: [ ],[ ]

Accepted Answer

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