A telemarketing firm has studied the effects of two factors on the response to i

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 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 table below.

Perform graphical analysis to check for interaction between time of day and position of advertisement. Then test for interaction with = .05.

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.)

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.)

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.)

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 output in table below.

Explanation / Answer

<I have answered the first 4 sub parts as per the answering guidelines. If you want the answers to the other parts of the problem also, please post the remaining parts seperately as another question>

a. The plotted graphs show that the effect of Time of Day is independent of the Time within program. The advertisement has more effect in the evening shows for all time in shows. Had the time within show have some effect on the time of day then the graphs would have intersected. However here there is a clear ranking of time in day--> evening > afternoon > morning for all possible time in show. So there is no interaction. This fact is confirmed by the F-statistic value and p-value calculation. The null hypotheses for annova is always that Ho: there is no interaction. The p-value for this test is 0.6089. So we accept H0. (we reject H0 only if p-value < 0.05). I.e we accept that there in no interaction.

The answer line options should be like: Accept H0: there is no interaction Graphical analysis supports the above conclusion.

(b) Here the H0: time of day is important. (Ideally it should be Time of day is not important - then given p-value<0.05, we reject the hypotheses to infer that Time of day actually has some effect). However p-value is <0.05 which means we reject the Null hypotheses. So the answer should be Reject.

(c) Here the H0: time within show position is important. (Ideally it should be time within show position is not important - then given p-value<0.05, we reject the hypotheses to infer that time within show position actually has some effect). However p-value is <0.05 which means we reject the Null hypotheses. So the answer should be Reject.

(d) We have got the Tukey's measure to 3.53. Under large sample assumption (there are 800 observation) Tukey's Q follows a N(0,1) distribution. We reject H0: there is no difference between the means if Q>1.96, the upper 95% value of N(0,1) distribution. So here 3.53 > 1.96 and hence we reject H0: all day times are same.

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