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6 Hypothesis Testing Questions

Problem 14.3
The marketing manager of a large supermarket chain would like to determine the effect of shelf space on the sales of pet food. A random sample of 12 equal-sized stores is selected, with the following results:

(see attachment for clearer tables)

Store Shelf Space X (Feet) Weekly Sales Y
(Hundreds of Dollars)
1 5 1.6
2 5 2.2
3 5 1.4
4 10 1.9
5 10 2.4
6 10 2.6
7 15 2.3
8 15 2.7
9 15 2.8
10 20 2.6
11 20 2.9
12 20 3.1

a. Set up a scatter diagram (NOTE: you can select this as an output with eth regression).
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b. Assuming a linear relationship, use the least squares method to find the regression coefficients B0 & B1.
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c. Interpret the meaning of slope (B1) in this problem.
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d. Predict the average weekly sales (in hundreds of dollars) of pet food for stores with 8 feet of shelf space for pet food.
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e. Suppose that sales in store 12 are 2.6. Repeat b-d with this value and compare the results to your original results.
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f. How much shelf space would you recommend that the marketing manager allocate to pet food? Explain..
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Problem 14.14
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Using the computer output you obtained to solve that problem.

a. Determine the coefficient of determination r2 and interpret its meaning.
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b. Determine the standard error of the estimate.
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c. How useful do you think this regression model is for predicting sales?
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Problem 14.22
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Perform a residual analysis for these data. Based on the results obtained,

a. Determine the adequacy of fit of the model.
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b. Evaluate whether the assumptions of regression have been seriously violated.
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Problem 14.30
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales.

a. Is it necessary to compute the Durbin Watson statistic? Explain.
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b. Under what circumstance would it be necessary to compute the Durbin Watson statistics before proceeding with the least squares method of regression analysis?
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Problem 14.37
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales. Using the output you obtained to solve that problem.

a. At the .05 level of significance, is there evidence of a linear relationship between shelf space and sales?
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Problem 14.51
In problem 14.3 (above), the marketing manager used shelf space for pet food to predict weekly sales.

a. Set up a 95% confidence interval estimate of the average weekly sales for all stores that have 8 feet of shelf space for pet food.
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b. Set up a 95% confidence interval estimate of the average weekly sales of an individual store that has 8 feet of shelf space for pet food.
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c. Explain the difference in the results obtained in a & b..
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