Question 1. Using the data below, compute A. Mean, B. Median and C. Mode D. Standard Deviation
15, 12, 30, 28, 50, 19, 75, 89, 41, 95, 67, 98, 53, 48, 19, 10
E. Construct a frequency and a relative frequency distribution using the following data classifications:
classes
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
F. Answer the following questions:
a. What is the shape of the data?
b. Do we have any outliers?
Question 2.
A. Amazon has looked at the metric average time on site per web visitor, and they have found that the average time on site is 4.25 minutes with a standard deviation of 2.1 minutes. The data follows a normal distribution. What proportion of visitors spend more than 3 minutes on the site?
B. If Amazon wanted to increase the time on site to those visitors who spend the least amount of time on the site by giving them special offers, what would be the amount of time on site that defines those customers who rank in the bottom 15% in terms of time on site?
Question 3. An analyst for Boston Common Apparel was asked to compare results from a recent marketing test from the latest catalog. She was concerned with three test panels and associated statistics.
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Panel
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Description
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Mail Qty
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Avg $ paid
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Std. Dev. $ paid
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Test 1
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Control Creative plus lift note from Corporate president
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9560
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$9.25
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$2.83
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Test 2
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New Creative
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9750
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$9.36
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$2.97
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|
Control
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Control creative only (no lift note)
|
10,005
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$9.08
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$2.20
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A. Complete the following steps to conduct a hypothesis test that the average dollars paid for the two test executions are the same versus the alternative that the tests yield different results.
(i) State the hypothesis
(ii) Compute the test statistic
(iii) Compute the p-value
(iv) What decision would you make at ? = 0.01?
B. Create a 95% Confidence interval for the difference in the mean dollars paid for
(i) Test 1 and the control panel.
(ii) Interpret fully the confidence interval you created in part B (i) Remember that you need to clearly explain things for the marketing team
Question 4 True or False
Answer each of the following questions as True or False. If the statement is false provide a brief explanation as to why it is false.
A. When calculating the required sample size for a population proportion a conservative approach if the true population proportion is unknown is to use p=0.50.
B. If in computing a hypothesis test your test statistic has a p-value of .015 you will accept Ho at ρ = 0.05.
C. In analyzing the distributional properties of quantitative data, if the mean and median are equal or nearly equal, the distribution will be symmetric.
D. If, for any given data set, a value of 5 is added to each observation, the resulting mean and standard deviation will also increase by five units.
E. Primary Market Research is market research data that is delivered routinely via a subscription.
Question 5.
A financial institution who markets home equity loans is testing two creatives, two interest rates, and 6 lists.
Specifically the creatives are: A. "Now the best time for a home equity loan"
B. "Hurry get a home equity loan before rates go up"
The loan terms are: 1. 6.75% APR with 3 points at closing
2. 7.25% APR with 1.5 points at closing
The Lists are List I
List II
List III
List IV
List V
List VI
Total test quantity is 50,000
The preliminary design is shown below:
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|
A. Now is the best time for a home equity loan
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B. Hurry get a home equity loan before rates go up
|
|
List
|
6.75% APR
|
7.25% APR
|
6.75% APR
|
7.25% APR
|
|
I
|
2083
|
2083
|
2083
|
2083
|
|
II
|
2083
|
2083
|
2083
|
2083
|
|
III
|
2083
|
2083
|
2083
|
2083
|
|
IV
|
2083
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2083
|
2083
|
2083
|
|
V
|
2083
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2083
|
2083
|
2083
|
|
VI
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2083
|
2083
|
2083
|
2083
|
Answer the questions shown below
A. What is the name of the test design shown above?
B. If the financial institution receives a response rate of 1.05% (.0105), for one of the cells provide an assessment of how precisely we can estimate a roll out response at a 95% level of confidence. (create a confidence interval around a proportion)
C. Do you think that the financial institution will see interactions in the factors in this test? Explain your reasoning completely.
5. (Continued)
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A. Now is the best time for a home equity loan
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B. Hurry get a home equity loan before rates go up
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|
List
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6.75% APR
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7.25% APR
|
6.75% APR
|
7.25% APR
|
|
I
|
|
|
|
|
|
II
|
|
|
|
|
|
III
|
|
|
|
|
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IV
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|
|
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V
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|
|
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VI
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|
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D. If it is believed that there is no interaction between the creatives, the loan terms and the lists, propose an alternative test design. Consider a main effects design. Indicate in the matrix below which cells are retained and give the reallocated samples size.
E. For your alternative test design, provide a comparison to the precision (by calculating a confidence interval around the proportion) for a cell receiving a response rate of 1.05% to the preliminary test design.
F. Compare the precision you calculated in part B to the precision calculated in part E. Explain the difference and what it means for each test design.