Question

Your marketing department believes it has a new commercial that will increase the percent of people who plan on purchasing from one of your stores in the next month. You take a sample of people and before you show them the new commercial, ask them if they are planning on purchasing from one of your stores in the next month. You then show them the new commercial and follow up by asking again if they plan on purchasing from one of your stores in the next month. In your data analysis, you look at the difference of (post-commercial)-(pre-commercial). You want to test the claim that there is no difference between the pre and post commercial mean percentages, and do so at the α=0.02α=0.02 level.

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

pre-commercial	post-commercial
55.6	54.1
53.3	40.3
75.6	67
49	81.1
52.3	79
58.8	-44.7
67.7	78.7
63.5	-47
55.8	24.2
58.2	27.7
52.3	81.6
63.5	74.5
38.4	4.8
45.8	25.4
50.5	34.3
45.8	-21.9
48.7	7.8
51.3	9.3
65.6	94.9
62.9	37.4
63.7	24.9
47.2	26.8
60.7	23
68.8	93.1
56	52

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample? Round to 4 decimal places.
   
   p-value =
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the mean difference is not equal to 0.
   • There is not sufficient evidence to warrant rejection of the claim that the mean difference is not equal to 0.
   • The sample data support the claim that the mean difference is not equal to 0.
   • There is not sufficient sample evidence to support the claim that the mean difference is not equal to 0.

Answer 1