Statisctics
Activity 1 CLO 1, CLO 2, CLO 3, CLO 4
1. Ball bearing manufacturing is a highly precise business in which minimal part variability is critical. Large variances in the size of the ball bearings cause bearing failure and rapid wear-out. Production standards call for a maximum variance of .0001 inches. Gerry Liddy has gathered a sample of 15 bearings that shows a sample standard deviation of .014 inches. Use ? = .10
a. Please determine whether the sample indicates that the maximum acceptable variance is being exceeded.
b. What is the p value?
2. The grade point averages of 352 students who completed a college course in financial accounting have a standard deviation of .940. The grade point averages of 73 students who dropped out of the same course have a standard deviation of .797.
a. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out?
b. Use ? = .05 level of significance.
c. What is the p value?
Note: F of alpha / 2 with degrees of freedom 351 and 72 which yields 0.025 area under its graph to the right is 1.466
Activity 2 CLO 1, CLO 2, CLO 3, CLO 4
This Activity requires a detailed analysis and to provide the answer to the three questions below:
1. As listed by The Arts Newspapers Visitor Figures Survey (https://www.theartnewspaper.com/visitor-figures-2017), the five most-visited art museums in the world, provided in Table 1 are the Louvre Museum, the National Museum in China, the Metropolitan Museum of Art, the Vatican Museums, and the British Museum.
Table 1
Frequencies of Ratings of the Museums by the Visitors Included in the Sample
Louvre
National Museum in China
Metropolitan Museum of Art
Vatican Museums
British Museum
Spectacular
113
88
94
98
96
Not spectacular
37
44
46
72
64
Use the sample data provided in the Table 1 to answer the following questions:
a. Calculate the point estimate of the population proportion of visitors who rated each of these museums as spectacular.
b. Conduct a hypothesis test to determine if the population proportion of visitors who rated the museum as spectacular is equal for these five museums using ? = .05 level of significance. What is the p-value?
c. If the null is rejected perform post-hoc test(s) using same ? and make conclusions.
0. A Financial Times/Harris Poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. The data in Table 2 is a portion of the polls findings concerning whether people favor or oppose the building of new nuclear power plants.
Table 2
The Frequencies of the Respondents Opinion about a New Nuclear Power Plant by Country of Origin.
Great Britain
France
Italy
Spain
Germany
United States
Strongly favor
141
161
298
133
128
204
Favor more than oppose
348
366
309
222
272
326
Oppose more than favor
381
334
219
311
322
316
Strongly oppose
217
215
219
443
398
174
Use the sample data provided in the Table 2 to answer the following questions:
a. How large was the sample in this poll?
b. Conduct a hypothesis test to determine whether peoples attitude toward building new nuclear power plants is independent of country using ? = .05 level of significance. What is the p-value and what is your conclusion?
c. Using the percentage of respondents who strongly favor and favor more than oppose, which country has the most favorable attitude toward building new nuclear power plants? Which country has the least favorable attitude?
0. Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus (New York Daily News, http://www.nydailynews.com/autos/street-smarts/best-selling-small-cars-2016-list-article-1.2945432). The 2017 market shares are: Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models making up the remaining 23%.
A sample of 400 compact car sales in Chicago showed the number of vehicles sold in Table 3.
Table 3
The Frequencies of Sales of Car Brands
Honda Civic
98
Toyota Corolla
72
Nissan Sentra
54
Hyundai Elantra
44
Chevrolet Cruze
42
Ford Focus
25
Others
65
Use a goodness of fit test to determine if the sample data indicate that the market shares for compact cars in Chicago are different than the market shares suggested by nationwide 2017 sales using ? = .05 level of significance.
a. What is the p-value and what is your conclusion?
b. If the Chicago market appears to differ significantly from the nationwide sales, which categories contribute most to this difference?
Activity 3 CLO 5, CLO 11, CLO 12
The Tire Rack, Americas leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 being the highest rating) for 18 maximum performance summer tires. The variable Steering rates, the tires steering responsiveness, Tread Wear rates, quickness of wear based on the drivers expectations, and Buy Again rates the drivers overall tire satisfaction and desire to purchase the same tire again. Values shown below are averages as obtained from surveys.
Table 4
Sample of Ratings of Eighteen Maximum Performance Summer Tires.
Tire
Steering
Treadwear
Buy Again
Goodyear Assurance TripleTred
8.9
8.5
8.1
Michelin HydroEdge
8.9
9.0
8.3
Michelin Harmony
8.3
8.8
8.2
Dunlop SP 60
8.2
8.5
7.9
Goodyear Assurance ComforTred
7.9
7.7
7.1
Yokohama Y372
8.4
8.2
8.9
Yokohama Aegis LS4
7.9
7.0
7.1
Kumho Power Star 758
7.9
7.9
8.3
Goodyear Assurance
7.6
5.8
4.5
Hankook H406
7.8
6.8
6.2
Michelin Energy LX4
7.4
5.7
4.8
Michelin MX4
7.0
6.5
5.3
Michelin Symmetry
6.9
5.7
4.2
Kumho 722
7.2
6.6
5.0
Dunlop SP 40 A/S
6.2
4.2
3.4
Bridgestone Insignia SE20
5.7
5.5
3.6
Goodyear Integrity
5.7
5.4
2.9
Dunlop SP20 FE
5.7
5.0
3.3
Use the data provided in Table 4 to answer the following questions:
1. Provide descriptive statistics of the data.
2. Develop two simple regression models that can be used to predict the Buy Again rating given the Steering Rating in one and the Tread Wear rating in the other. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model.
3. Develop a multiple regression model that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
4. Does combining the two independent variables improve coefficient of determination? Please explain.
5. Choose a combination of steering and treadwear not given in the above table and find the expected Buy Again for this combination.
Activity 6 – CLO 4, CLO 7, CLO 8, CLO 11, CLO 12
A research firm tests the miles per gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) provided in Table 8.
Table 8
The Results of the Experiment (miles per gallon)
Gasoline Brands
I
II
III
Automobiles
A
18
21
20
B
24
26
27
C
30
29
34
D
22
25
24
E
20
23
24
Use the sample data provided in the Table 8 to answer the following questions:
1. Provide descriptive statistics of the data divided according to the division in gasoline brand.
2. Formulate a single factor ANOVA hypothesis test, with gasoline brand being the factor. Perform the test, interpret the result, and include all phases of ANOVA.
3. Analyze the data using the ANOVA procedure for completely randomized designs and include all phases of the test. Compare your findings with those obtained in question (a). What is the advantage of attempting to remove the block effect?
4. Perform post-hoc tests for rank ordering, if applicable.
Use ? = .05 in all tests. Perform the tests once manually and once using SPSS.
Professional Assignment 1 CLO 3, CLO 5, CLO 6, CLO 11, CLO 12
Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users are given in Table 5. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers.
a. Provide descriptive statistics of the data, develop a multiple regression model that can be used to predict the Amount Charged given the Annual Income and Household Size, state the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
b. To assess robustness of the software, repeat part (a) but this time use full representation of Annual Income. What conclusions can you make?
c. Choose a combination of Annual Income and Household Size not given in the table and find the expected Amount Charged for this combination.
Use ? = .05 in testing all hypotheses
Table 5
Data on Annual Income, Household size, Amount of Credit Changed
Income ($1000s)
Household size
Amount charged ($)
Income
Size
Charged
54
3
4016
54
6
5573
30
2
3159
30
1
2583
32
4
5100
48
2
3866
50
5
4742
34
5
3586
31
2
1864
67
4
5037
55
2
4070
50
2
3605
37
1
2731
67
5
5345
40
2
3348
55
6
5370
66
4
4764
52
2
3890
51
3
4110
62
3
4705
25
3
4208
64
2
4157
48
4
4219
22
3
3579
27
1
2477
29
4
3890
33
2
2514
39
2
2972
65
3
4214
35
1
3121
63
4
4965
39
4
4183
42
6
4412
54
3
3730
21
2
2448
23
6
4127
44
1
2995
27
2
2921
37
5
4171
26
7
4603
62
6
5678
61
2
4273
21
3
3623
30
2
3067
55
7
5301
22
4
3074
42
2
3020
46
5
4820
41
7
4828
66
4
5149
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Home>Mathematics homework help>Statistics homework help>Statisctics
Activity 1 CLO 1, CLO 2, CLO 3, CLO 4
1. Ball bearing manufacturing is a highly precise business in which minimal part variability is critical. Large variances in the size of the ball bearings cause bearing failure and rapid wear-out. Production standards call for a maximum variance of .0001 inches. Gerry Liddy has gathered a sample of 15 bearings that shows a sample standard deviation of .014 inches. Use ? = .10
a. Please determine whether the sample indicates that the maximum acceptable variance is being exceeded.
b. What is the p value?
2. The grade point averages of 352 students who completed a college course in financial accounting have a standard deviation of .940. The grade point averages of 73 students who dropped out of the same course have a standard deviation of .797.
a. Do the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out?
b. Use ? = .05 level of significance.
c. What is the p value?
Note: F of alpha / 2 with degrees of freedom 351 and 72 which yields 0.025 area under its graph to the right is 1.466
Activity 2 CLO 1, CLO 2, CLO 3, CLO 4
This Activity requires a detailed analysis and to provide the answer to the three questions below:
1. As listed by The Arts Newspapers Visitor Figures Survey (https://www.theartnewspaper.com/visitor-figures-2017), the five most-visited art museums in the world, provided in Table 1 are the Louvre Museum, the National Museum in China, the Metropolitan Museum of Art, the Vatican Museums, and the British Museum.
Table 1
Frequencies of Ratings of the Museums by the Visitors Included in the Sample
Louvre
National Museum in China
Metropolitan Museum of Art
Vatican Museums
British Museum
Spectacular
113
88
94
98
96
Not spectacular
37
44
46
72
64
Use the sample data provided in the Table 1 to answer the following questions:
a. Calculate the point estimate of the population proportion of visitors who rated each of these museums as spectacular.
b. Conduct a hypothesis test to determine if the population proportion of visitors who rated the museum as spectacular is equal for these five museums using ? = .05 level of significance. What is the p-value?
c. If the null is rejected perform post-hoc test(s) using same ? and make conclusions.
0. A Financial Times/Harris Poll surveyed people in six countries to assess attitudes toward a variety of alternate forms of energy. The data in Table 2 is a portion of the polls findings concerning whether people favor or oppose the building of new nuclear power plants.
Table 2
The Frequencies of the Respondents Opinion about a New Nuclear Power Plant by Country of Origin.
Great Britain
France
Italy
Spain
Germany
United States
Strongly favor
141
161
298
133
128
204
Favor more than oppose
348
366
309
222
272
326
Oppose more than favor
381
334
219
311
322
316
Strongly oppose
217
215
219
443
398
174
Use the sample data provided in the Table 2 to answer the following questions:
a. How large was the sample in this poll?
b. Conduct a hypothesis test to determine whether peoples attitude toward building new nuclear power plants is independent of country using ? = .05 level of significance. What is the p-value and what is your conclusion?
c. Using the percentage of respondents who strongly favor and favor more than oppose, which country has the most favorable attitude toward building new nuclear power plants? Which country has the least favorable attitude?
0. Based on 2017 sales, the six top-selling compact cars are the Honda Civic, Toyota Corolla, Nissan Sentra, Hyundai Elantra, Chevrolet Cruze, and Ford Focus (New York Daily News, http://www.nydailynews.com/autos/street-smarts/best-selling-small-cars-2016-list-article-1.2945432). The 2017 market shares are: Honda Civic 20%, Toyota Corolla 17%, Nissan Sentra 12%, Hyundai Elantra 10%, Chevrolet Cruze 10%, and Ford Focus 8%, with other small car models making up the remaining 23%.
A sample of 400 compact car sales in Chicago showed the number of vehicles sold in Table 3.
Table 3
The Frequencies of Sales of Car Brands
Honda Civic
98
Toyota Corolla
72
Nissan Sentra
54
Hyundai Elantra
44
Chevrolet Cruze
42
Ford Focus
25
Others
65
Use a goodness of fit test to determine if the sample data indicate that the market shares for compact cars in Chicago are different than the market shares suggested by nationwide 2017 sales using ? = .05 level of significance.
a. What is the p-value and what is your conclusion?
b. If the Chicago market appears to differ significantly from the nationwide sales, which categories contribute most to this difference?
Activity 3 CLO 5, CLO 11, CLO 12
The Tire Rack, Americas leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 being the highest rating) for 18 maximum performance summer tires. The variable Steering rates, the tires steering responsiveness, Tread Wear rates, quickness of wear based on the drivers expectations, and Buy Again rates the drivers overall tire satisfaction and desire to purchase the same tire again. Values shown below are averages as obtained from surveys.
Table 4
Sample of Ratings of Eighteen Maximum Performance Summer Tires.
Tire
Steering
Treadwear
Buy Again
Goodyear Assurance TripleTred
8.9
8.5
8.1
Michelin HydroEdge
8.9
9.0
8.3
Michelin Harmony
8.3
8.8
8.2
Dunlop SP 60
8.2
8.5
7.9
Goodyear Assurance ComforTred
7.9
7.7
7.1
Yokohama Y372
8.4
8.2
8.9
Yokohama Aegis LS4
7.9
7.0
7.1
Kumho Power Star 758
7.9
7.9
8.3
Goodyear Assurance
7.6
5.8
4.5
Hankook H406
7.8
6.8
6.2
Michelin Energy LX4
7.4
5.7
4.8
Michelin MX4
7.0
6.5
5.3
Michelin Symmetry
6.9
5.7
4.2
Kumho 722
7.2
6.6
5.0
Dunlop SP 40 A/S
6.2
4.2
3.4
Bridgestone Insignia SE20
5.7
5.5
3.6
Goodyear Integrity
5.7
5.4
2.9
Dunlop SP20 FE
5.7
5.0
3.3
Use the data provided in Table 4 to answer the following questions:
1. Provide descriptive statistics of the data.
2. Develop two simple regression models that can be used to predict the Buy Again rating given the Steering Rating in one and the Tread Wear rating in the other. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model.
3. Develop a multiple regression model that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
4. Does combining the two independent variables improve coefficient of determination? Please explain.
5. Choose a combination of steering and treadwear not given in the above table and find the expected Buy Again for this combination.
Activity 6 – CLO 4, CLO 7, CLO 8, CLO 11, CLO 12
A research firm tests the miles per gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) provided in Table 8.
Table 8
The Results of the Experiment (miles per gallon)
Gasoline Brands
I
II
III
Automobiles
A
18
21
20
B
24
26
27
C
30
29
34
D
22
25
24
E
20
23
24
Use the sample data provided in the Table 8 to answer the following questions:
1. Provide descriptive statistics of the data divided according to the division in gasoline brand.
2. Formulate a single factor ANOVA hypothesis test, with gasoline brand being the factor. Perform the test, interpret the result, and include all phases of ANOVA.
3. Analyze the data using the ANOVA procedure for completely randomized designs and include all phases of the test. Compare your findings with those obtained in question (a). What is the advantage of attempting to remove the block effect?
4. Perform post-hoc tests for rank ordering, if applicable.
Use ? = .05 in all tests. Perform the tests once manually and once using SPSS.
Professional Assignment 1 CLO 3, CLO 5, CLO 6, CLO 11, CLO 12
Consumer Research, Inc., is an independent agency that conducts research on consumer attitudes and behaviors for a variety of firms. In one study, a client asked for an investigation of consumer characteristics that can be used to predict the amount charged by credit card users are given in Table 5. Data were collected on annual income, household size, and annual credit card charges for a sample of 50 consumers.
a. Provide descriptive statistics of the data, develop a multiple regression model that can be used to predict the Amount Charged given the Annual Income and Household Size, state the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
b. To assess robustness of the software, repeat part (a) but this time use full representation of Annual Income. What conclusions can you make?
c. Choose a combination of Annual Income and Household Size not given in the table and find the expected Amount Charged for this combination.
Use ? = .05 in testing all hypotheses
Table 5
Data on Annual Income, Household size, Amount of Credit Changed
Income ($1000s)
Household size
Amount charged ($)
Income
Size
Charged
54
3
4016
54
6
5573
30
2
3159
30
1
2583
32
4
5100
48
2
3866
50
5
4742
34
5
3586
31
2
1864
67
4
5037
55
2
4070
50
2
3605
37
1
2731
67
5
5345
40
2
3348
55
6
5370
66
4
4764
52
2
3890
51
3
4110
62
3
4705
25
3
4208
64
2
4157
48
4
4219
22
3
3579
27
1
2477
29
4
3890
33
2
2514
39
2
2972
65
3
4214
35
1
3121
63
4
4965
39
4
4183
42
6
4412
54
3
3730
21
2
2448
23
6
4127
44
1
2995
27
2
2921
37
5
4171
26
7
4603
62
6
5678
61
2
4273
21
3
3623
30
2
3067
55
7
5301
22
4
3074
42
2
3020
46
5
4820
41
7
4828
66
4
5149
Applied Sciences
Architecture and Design
Biology
Business & Finance
Chemistry
Computer Science
Geography
Geology
Education
Engineering
English
Environmental science
Spanish
Government
History
Human Resource Management
Information Systems
Law
Literature
Mathematics
Nursing
Physics
Political Science
Psychology
Reading
Science
Social Science
Liberty University
New Hampshire University
Strayer University
University Of Phoenix
Walden University
Home
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Archive
Tags
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