3 A telemarketing firm has studied the effects of two factors on the response to
ID: 3149357 • Letter: 3
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3 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 Source of Variation SS df MS F P-Value F crit Rows (Time) 21560.89 2 10780.444 1209.02 8.12E-25 3.403 Columns (Position) 3989.42 3 1329.B06 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 a. Test the significance of time of day effects with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using critical value approach): b. Test the significance of position of advertisement effects with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using p-value approach): c. Test the significance of interaction between time of day and position of advertisement with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using critical value approach): Research and explain how we can use the interaction plot above to visually test for the significance of interaction. What is your conclusion for this particular problem using graphical analysis? Attach an additional page for your answer to the bonus question (Please note that there is no partial credit for the bonus question.) 3 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 Source of Variation SS df MS F P-Value F crit Rows (Time) 21560.89 2 10780.444 1209.02 8.12E-25 3.403 Columns (Position) 3989.42 3 1329.B06 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 a. Test the significance of time of day effects with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using critical value approach): b. Test the significance of position of advertisement effects with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using p-value approach): c. Test the significance of interaction between time of day and position of advertisement with = .05. F-statistic = p-value = Critical Value = Conclusion (State the rejection rule using critical value approach): Research and explain how we can use the interaction plot above to visually test for the significance of interaction. What is your conclusion for this particular problem using graphical analysis? Attach an additional page for your answer to the bonus question (Please note that there is no partial credit for the bonus question.)Explanation / Answer
a) Test of significance of time of day effects with = .05.
F-statistic = 1209.02
p-value = 8.12*e-25
Critical Value = 3.403
We will reject the null hypothesis that the mean responses of television advertisements on different times are all same,i.e there is no effect of time on ad response, if the observed F-statistics > Critical value.
As F-statistics > Critical value, we can say that there is enough evidence to reject the null hypothesis and conclude that there is effect of time on ad response.
b) Test of significance of time of day effects with = .05.
F-statistic = 149.14
p-value = 1.19*e-15
Critical Value = 3.009
We will reject the null hypothesis that the mean responses of television advertisements depends on the position of the ad within the hour are all same,i.e there is no effect of the position of the ad within the hour on ad response, if the observed F-statistics > Critical value.
As F-statistics > Critical value, we can say that there is enough evidence to reject the null hypothesis and conclude that there is effect of the position of the ad within the hour on ad response.
c) Test of significance of interaction between time of day and position of advertisement with = .05.
F-statistic = 0.47
p-value = 0.8212
Critical Value = 2.508
We will reject the null hypothesis that the mean responses of television advertisements due to the interaction of time and position of the ad within the hour are all same,i.e there is no effect due to the interaction of time and the position of the ad within the hour on ad response, if the observed F-statistics > Critical value.
As F-statistics < Critical value, we can say that there is not enough evidence to reject the null hypothesis and conclude that there is effect due to the interaction of time and position of the ad within the hour.
d) Use of Interaction plot to test the significance of interaction effect
We can also use interaction plot to visually test for the significance of interaction. If the lines in the interaction plot are not parallel, or if the bars in a bar diagram are not relative same then we can say there is interaction effect of the main factors in the data.
The following is a plot of the data-
In the above plot we can see that the lines for all the four different postions of the advertisement are almost parallel to each other.
The following is a bar diagram of the data-
In the above graph also, we can see the plots for different position of advertisement are all relatively same from 10:00 morning to 9:00 evening. So there is no interaction effect of any time and position of advertisement.
From the graph we can say that, from 10:00 morning to 9:00 evening, the ad response increases for all positions of advertisement. But as the lines are almost parallel to each other, so there is no significant added effect(i.e interaction effect) or the interaction effect is not significant.
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