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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

(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. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(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.)

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