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A CD manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?
A. It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment.
B. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because there was no control group for comparison.
C. It is NOT reasonable to conclude that the difference in sales was caused the different cover designs because the 70 stores were not randomly chosen.
D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.
E. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.

Respuesta :

Answer:

The statement that gives the best conclusion that should be made based on the results and provides the best explanation for the conclusion is option D;

D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores

Step-by-step explanation:

The data given in the question are presented as follows;

The particulars the CD manufacturer wants to determine = The CD cover design that will generate more sales

The mode of selection of the stores for the test = Random selection

The number of stores in each group of stores, n = 35 stores

The number of sets of stores tested = 2 sets of stores

Let [tex]\overline x_1[/tex] represent the mean number CDs sold at one set of stores and [tex]\overline x_2[/tex] represent the mean number CDs sold at the other set of stores

The null hypothesis, H₀; [tex]\overline x_1[/tex] = [tex]\overline x_2[/tex]

The alternative hypothesis, H₀; [tex]\overline x_1[/tex] ≠ [tex]\overline x_2[/tex]

Given that the statistical analysis shows that the difference in mean between the two sets of randomly selected stores is significant, we therefore should reject the null hypothesis and accept the alternative hypothesis that there is a significant difference in CD sale attributable to the difference in cover design as the CDs having on of two cover design where assigned randomly to the stores.

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