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.)

Position of Advertisement   Time of Day On the Hour On the Half-Hour Early in Program Late in Program   10:00 morning 43          37           62            50           35          42           68            46           40          39           66            50             4:00 afternoon 62          57           86            68           60          64           81            60           60          53           80            67             9:00 evening 105          95           127            103           96          99           119            101           102          102           128            109          

Explanation / Answer

# i will answer 1st 4 subparts #

a) by looking at the graph one can comment that there is no interaction between variables

b) p-value>0.05 hence we fail to reject that there is no interaction.

c)Test the significance of position of advertisement effects with = .05.

F = 84.28, p-value = less than .001

pvalue<0.05 reject H0: position of the ads is important

d) margin of error=E=5.48

then  CI for uM – uA:=(67-65.33-5.48,67-65.33+5.48)=(-3.81,7.81)

then  CI for uM – uE:=(67-90.78-5.58,67-90.78+5.58)=(-29.26,-18.3)

then  CI for uA – uE:=(65.33-90.75-5.48,65.33-90.75-5.48)=(-30.93,-19.97)

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