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Confidence Interval,Hypothesis Testing & Regression Analysis

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The Skaff Appliance Company currently has over 1,000 retail outlets throughout the United States and Canada. They sell name brand electronic products, such as TVs, stereos, VCRs, and microwave ovens. Skaff Appliance is considering opening several additional stores in other large metropolitan areas. Paul Skaff, president, would like to study the relationship between the sales at existing locations and several factors regarding the existing store or its region. The factors are the population and the unemployment in the region, and the advertising expense of the store. Another variable considered is 'mall'. Mall refers to whether the existing store is located in an enclosed shopping mall or not. A '1' indicates a mall location; a '0' indicates the store is not located in a mall. A random sample of 20 stores is selected.

Sales
(000)

Population
(000,000)

Percent
Unemployed
Advertising
Expense
(000)

Mall
Location
5.17
7.50
5.1
59.0
0
5.78
8.71
6.3
62.5
0
4.84
10.00
4.7
61.0
0
6.00
7.45
5.4
61.0
1
6.00
8.67
5.4
61.0
1
6.12
11.00
7.2
12.5
0
6.40
13.18
5.8
35.8
0
7.10
13.81
5.8
59.9
0
8.50
14.43
6.2
57.2
1
7.50
10.00
5.5
35.8
0
9.30
13.21
6.8
27.9
0
8.80
17.10
6.2
24.1
1
9.96
15.12
6.3
27.7
1
9.83
18.70
0.5
24.0
0
10.12
20.20
5.5
57.2
1
10.70
15.00
5.8
44.3
0
10.45
17.60
7.1
49.2
0
11.32
19.80
7.5
23.0
0
11.87
14.40
8.2
62.7
1
11.91
20.35
7.8
55.8
0

Managerial Report

1. Construct the confidence interval for the mean of sales of stores for this company.
2. Are mean of sales different between stores which are located in the malls and not located in the malls?
3. Compare the mean of advertising expense of the stores which are located in the malls and the stores which are not located in the malls
4. What is the confidence interval for the proportion of the stores having the advertising expense which are larger than or equals to 50,000 (USD)
5. Using the data given, estimate the multiple linear regression equation of the dependence of sales on Population, Unemployment Rate, Advertising Expense and Mall Location. Answer the following questions:

a. Write down the estimated regression model and explain the meaning of each estimated regression coefficients?
b. What is the value of multiple coefficient of determination and explain its meaning?
c. What independence variable (s) which is not significant in the model
d. Testing for overall significance of the model?
e. Whether or not the Mall Location affect on sales of the stores
f. What is the estimated value of sales of a store which is located in a mall, in a region with unemployment rate 4%, population 18,000,000 and this store invests 40,000 (USD) for advertising?

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Solution Summary

The solution provides step by step method for the calculation of confidence intervals, testing of hypothesis and multiple regression analysis. Formula for the calculation and Interpretations of the results are also included.

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