Confidence Intervals

Scenario (information repeated for deliverable 01, 03, and 04)

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

A listing of the jobs by title

The salary (in dollars) for each job

Deliverable 3 – Confidence Intervals.xlsx

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

1.
Competency
Develop a confidence interval for a population parameter.
Student Success Criteria
View the grading rubric for this deliverable by selecting the “This item is graded with a rubric”
link, which is located in the Details & Information pane.
Instructions
Scenario (information repeated for deliverable 01, 03, and 04)
A major client of your company is interested in the salary distributions of jobs in the state of
Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks
you to research and analyze the salary distributions. You are given a spreadsheet that contains
the following information:
o A listing of the jobs by title
o The salary (in dollars) for each job
You have previously explained some of the basic statistics to your client already, and he really
liked your work. Now he wants you to analyze the confidence intervals.
Background information on the Data
The data set in the spreadsheet consists of 364 records that you will be analyzing from the
Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly
salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.
What to Submit
Your boss wants you to submit the spreadsheet with the completed calculations, answers, and
analysis.
Job Title
Accountants and Auditors
Actuaries
Administrative Law Judges, Adjudicators, and Hearing Officers
Administrative Services Managers
Adult Basic and Secondary Education and Literacy Teachers and Instructors
Advertising and Promotions Managers
Advertising Sales Agents
Aerospace Engineering and Operations Technicians
Aerospace Engineers
Agents and Business Managers of Artists, Performers, and Athletes
Agricultural and Food Science Technicians
Agricultural Inspectors
Agricultural Sciences Teachers, Postsecondary
Air Traffic Controllers
Aircraft Cargo Handling Supervisors
Aircraft Structure, Surfaces, Rigging, and Systems Assemblers
Airfield Operations Specialists
Airline Pilots, Copilots, and Flight Engineers
Anthropologists and Archeologists
Appraisers and Assessors of Real Estate
Arbitrators, Mediators, and Conciliators
Architects, Except Landscape and Naval
Architectural and Civil Drafters
Architecture and Engineering Occupations
Architecture Teachers, Postsecondary
Archivists
Art Directors
Art, Drama, and Music Teachers, Postsecondary
Athletic Trainers
Atmospheric and Space Scientists
Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary
Audiologists
Avionics Technicians
Biomedical Engineers
Boilermakers
Broadcast News Analysts
Brokerage Clerks
Budget Analysts
Business and Financial Operations Occupations
Business Operations Specialists, All Other
Business Teachers, Postsecondary
Buyers and Purchasing Agents, Farm Products
Camera and Photographic Equipment Repairers
Captains, Mates, and Pilots of Water Vessels
Cardiovascular Technologists and Technicians
Career/Technical Education Teachers, Middle School
Career/Technical Education Teachers, Secondary School
Cargo and Freight Agents
Cartographers and Photogrammetrists
Chefs and Head Cooks
Chemical Engineers
Chemical Equipment Operators and Tenders
Chemical Plant and System Operators
Chemical Technicians
Chemistry Teachers, Postsecondary
Chemists
Child, Family, and School Social Workers
Chiropractors
Civil Engineers
Claims Adjusters, Examiners, and Investigators
Clinical, Counseling, and School Psychologists
Coil Winders, Tapers, and Finishers
Commercial and Industrial Designers
Commercial Pilots
Communications Equipment Operators, All Other
Communications Teachers, Postsecondary
Community and Social Service Occupations
Community Health Workers
Compensation and Benefits Managers
Compensation, Benefits, and Job Analysis Specialists
Compliance Officers
Computer and Information Research Scientists
Computer and Information Systems Managers
Computer and Mathematical Occupations
Computer Hardware Engineers
Computer Network Architects
Computer Network Support Specialists
Computer Occupations, All Other
Computer Programmers
Computer Science Teachers, Postsecondary
Computer Systems Analysts
Computer User Support Specialists
Conservation Scientists
Construction and Building Inspectors
Construction Managers
Continuous Mining Machine Operators
Control and Valve Installers and Repairers, Except Mechanical Door
Conveyor Operators and Tenders
Cost Estimators
Crane and Tower Operators
Credit Analysts
Credit Counselors
Criminal Justice and Law Enforcement Teachers, Postsecondary
Curators
Database Administrators
Dental Hygienists
Derrick Operators, Oil and Gas
Detectives and Criminal Investigators
Diagnostic Medical Sonographers
Dietitians and Nutritionists
Directors, Religious Activities and Education
Drafters, All Other
Economics Teachers, Postsecondary
Economists
Editors
Education Administrators, All Other
Education Administrators, Elementary and Secondary School
Education Administrators, Postsecondary
Education Administrators, Preschool and Childcare Center/Program
Education Teachers, Postsecondary
Education, Training, and Library Occupations
Educational, Guidance, School, and Vocational Counselors
Electric Motor, Power Tool, and Related Repairers
Electrical and Electronics Drafters
Electrical and Electronics Engineering Technicians
Electrical and Electronics Installers and Repairers, Transportation Equipment
Electrical and Electronics Repairers, Commercial and Industrial Equipment
Electrical and Electronics Repairers, Powerhouse, Substation, and Relay
Electrical Engineers
Electrical Power-Line Installers and Repairers
Electricians
Electro-Mechanical Technicians
Electronics Engineers, Except Computer
Elementary School Teachers, Except Special Education
Elevator Installers and Repairers
Embalmers
Emergency Management Directors
Engineering Technicians, Except Drafters, All Other
English Language and Literature Teachers, Postsecondary
Environmental Engineering Technicians
Environmental Engineers
Environmental Science and Protection Technicians, Including Health
Environmental Science Teachers, Postsecondary
Environmental Scientists and Specialists, Including Health
Epidemiologists
Executive Secretaries and Executive Administrative Assistants
Exercise Physiologists
Explosives Workers, Ordnance Handling Experts, and Blasters
Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders
Farm and Home Management Advisors
Film and Video Editors
Financial Analysts
Financial Clerks, All Other
Financial Examiners
Financial Managers
Financial Specialists, All Other
Fire Inspectors and Investigators
Firefighters
First-Line Supervisors of Construction Trades and Extraction Workers
First-Line Supervisors of Correctional Officers
First-Line Supervisors of Farming, Fishing, and Forestry Workers
First-Line Supervisors of Fire Fighting and Prevention Workers
First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand
First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers
First-Line Supervisors of Mechanics, Installers, and Repairers
First-Line Supervisors of Non-Retail Sales Workers
First-Line Supervisors of Office and Administrative Support Workers
First-Line Supervisors of Police and Detectives
First-Line Supervisors of Production and Operating Workers
First-Line Supervisors of Protective Service Workers, All Other
First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators
Fish and Game Wardens
Food Service Managers
Foreign Language and Literature Teachers, Postsecondary
Forensic Science Technicians
Forest and Conservation Technicians
Foresters
Forestry and Conservation Science Teachers, Postsecondary
Fundraisers
Funeral Service Managers
Gaming Supervisors
Gas Compressor and Gas Pumping Station Operators
Gas Plant Operators
General and Operations Managers
Geography Teachers, Postsecondary
Geological and Petroleum Technicians
Geoscientists, Except Hydrologists and Geographers
Health and Safety Engineers, Except Mining Safety Engineers and Inspectors
Health Diagnosing and Treating Practitioners, All Other
Health Educators
Health Specialties Teachers, Postsecondary
Health Technologists and Technicians, All Other
Healthcare Practitioners and Technical Occupations
Healthcare Social Workers
Hearing Aid Specialists
Historians
History Teachers, Postsecondary
Hoist and Winch Operators
Home Economics Teachers, Postsecondary
Human Resources Managers
Human Resources Specialists
Industrial Engineering Technicians
Industrial Engineers
Industrial Machinery Mechanics
Industrial Production Managers
Information and Record Clerks, All Other
Information Security Analysts
Installation, Maintenance, and Repair Occupations
Instructional Coordinators
Insurance Appraisers, Auto Damage
Insurance Sales Agents
Insurance Underwriters
Interior Designers
Judges, Magistrate Judges, and Magistrates
Kindergarten Teachers, Except Special Education
Labor Relations Specialists
Landscape Architects
Lawyers
Layout Workers, Metal and Plastic
Legal Occupations
Legal Support Workers, All Other
Librarians
Library Science Teachers, Postsecondary
Life Scientists, All Other
Life, Physical, and Social Science Occupations
Loading Machine Operators, Underground Mining
Loan Officers
Locomotive Engineers
Logging Workers, All Other
Logisticians
Magnetic Resonance Imaging Technologists
Management Analysts
Managers, All Other
Marine Engineers and Naval Architects
Market Research Analysts and Marketing Specialists
Marketing Managers
Marriage and Family Therapists
Materials Engineers
Mathematical Science Teachers, Postsecondary
Mechanical Drafters
Mechanical Engineering Technicians
Mechanical Engineers
Media and Communication Equipment Workers, All Other
Medical and Clinical Laboratory Technologists
Medical and Health Services Managers
Medical Equipment Repairers
Meeting, Convention, and Event Planners
Mental Health Counselors
Metal-Refining Furnace Operators and Tenders
Middle School Teachers, Except Special and Career/Technical Education
Millwrights
Mine Cutting and Channeling Machine Operators
Mine Shuttle Car Operators
Mining and Geological Engineers, Including Mining Safety Engineers
Mining Machine Operators, All Other
Mixing and Blending Machine Setters, Operators, and Tenders
Mobile Heavy Equipment Mechanics, Except Engines
Model Makers, Metal and Plastic
Morticians, Undertakers, and Funeral Directors
Multimedia Artists and Animators
Music Directors and Composers
Natural Sciences Managers
Network and Computer Systems Administrators
Nuclear Engineers
Nuclear Medicine Technologists
Nuclear Technicians
Nurse Practitioners
Nursing Instructors and Teachers, Postsecondary
Occupational Health and Safety Specialists
Occupational Health and Safety Technicians
Occupational Therapists
Occupational Therapy Assistants
Operations Research Analysts
Optometrists
Orthotists and Prosthetists
Painters, Transportation Equipment
Paper Goods Machine Setters, Operators, and Tenders
Paralegals and Legal Assistants
Patternmakers, Metal and Plastic
Personal Financial Advisors
Petroleum Pump System Operators, Refinery Operators, and Gaugers
Pharmacists
Philosophy and Religion Teachers, Postsecondary
Physical Therapist Assistants
Physical Therapists
Physician Assistants
Physicists
Physics Teachers, Postsecondary
Plant and System Operators, All Other
Plumbers, Pipefitters, and Steamfitters
Podiatrists
Police and Sheriff’s Patrol Officers
Political Science Teachers, Postsecondary
Postal Service Clerks
Postal Service Mail Carriers
Postal Service Mail Sorters, Processors, and Processing Machine Operators
Postmasters and Mail Superintendents
Power Distributors and Dispatchers
Power Plant Operators
Precision Instrument and Equipment Repairers, All Other
Private Detectives and Investigators
Probation Officers and Correctional Treatment Specialists
Producers and Directors
Production, Planning, and Expediting Clerks
Property, Real Estate, and Community Association Managers
Psychologists, All Other
Psychology Teachers, Postsecondary
Public Relations and Fundraising Managers
Public Relations Specialists
Pump Operators, Except Wellhead Pumpers
Purchasing Agents, Except Wholesale, Retail, and Farm Products
Purchasing Managers
Radiation Therapists
Radio, Cellular, and Tower Equipment Installers and Repairers
Radiologic Technologists
Rail Yard Engineers, Dinkey Operators, and Hostlers
Railroad Conductors and Yardmasters
Rail-Track Laying and Maintenance Equipment Operators
Real Estate Brokers
Real Estate Sales Agents
Recreation and Fitness Studies Teachers, Postsecondary
Recreational Vehicle Service Technicians
Refractory Materials Repairers, Except Brickmasons
Registered Nurses
Reinforcing Iron and Rebar Workers
Respiratory Therapists
Rolling Machine Setters, Operators, and Tenders, Metal and Plastic
Roof Bolters, Mining
Rotary Drill Operators, Oil and Gas
Sales Engineers
Sales Managers
Sales Representatives, Services, All Other
Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products
Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products
Secondary School Teachers, Except Special and Career/Technical Education
Securities, Commodities, and Financial Services Sales Agents
Service Unit Operators, Oil, Gas, and Mining
Set and Exhibit Designers
Ship Engineers
Signal and Track Switch Repairers
Social and Community Service Managers
Social Scientists and Related Workers, All Other
Social Work Teachers, Postsecondary
Social Workers, All Other
Sociology Teachers, Postsecondary
Software Developers, Applications
Software Developers, Systems Software
Soil and Plant Scientists
Sound Engineering Technicians
Special Education Teachers, All Other
Special Education Teachers, Kindergarten and Elementary School
Special Education Teachers, Middle School
Special Education Teachers, Secondary School
Speech-Language Pathologists
Stationary Engineers and Boiler Operators
Statisticians
Surveyors
Tank Car, Truck, and Ship Loaders
Tax Examiners and Collectors, and Revenue Agents
Technical Writers
Telecommunications Equipment Installers and Repairers, Except Line Installers
Tire Builders
Tool and Die Makers
Training and Development Managers
Training and Development Specialists
Transportation Inspectors
Transportation, Storage, and Distribution Managers
Urban and Regional Planners
Veterinarians
Water and Wastewater Treatment Plant and System Operators
Web Developers
Wholesale and Retail Buyers, Except Farm Products
Writers and Authors
Zoologists and Wildlife Biologists
Salary
71,400
99,870
112,660
93,150
54,890
136,840
63,000
69,230
109,960
85,910
42,540
39,700
92,010
128,980
57,690
48,860
55,190
101,050
56,640
71,530
91,560
85,930
53,290
80,770
79,040
49,970
85,820
70,390
48,990
99,860
93,990
81,010
55,680
108,290
71,230
73,660
48,850
75,010
72,420
69,870
90,540
62,290
41,910
67,220
65,850
61,970
source: http://www.bls.gov/
Calculations/Values
Mean
Standard Deviation
n
Formulas/Answers
64,740
45,820
69,020
48,290
86,360
41,520
48,830
53,650
88,390
85,030
54,310
79,250
87,310
62,230
82,130
33,490
63,710
83,220
40,600
66,990
47,550
40,340
144,350
75,350
74,970
117,200
140,920
86,710
112,250
107,860
60,200
77,570
89,440
96,020
91,230
55,520
65,820
69,070
93,290
42,760
68,400
36,200
65,650
59,680
82,060
49,650
71,970
54,870
88,410
72,900
44,610
77,660
78,560
61,440
50,210
53,330
109,480
72,810
55,220
79,860
102,010
91,970
57,390
65,010
55,000
56,310
40,360
58,770
62,450
61,260
63,410
78,680
94,390
79,120
67,500
56,450
99,490
63,490
83,900
46,100
87,050
57,360
66,090
42,190
87,360
49,460
90,710
74,110
77,440
56,010
58,990
58,320
38,740
74,190
50,190
91,420
38,860
89,040
133,980
70,440
65,710
36,200
73,810
76,370
60,690
71,570
49,590
51,310
66,430
77,900
60,960
87,970
62,830
52,470
58,250
46,110
56,800
68,890
59,640
42,970
63,990
90,080
59,900
98,920
31,570
56,220
67,370
109,490
80,130
54,390
72,210
88,300
82,600
56,120
82,450
54,160
86,270
58,530
55,690
62,210
85,040
80,660
71,400
121,530
64,140
53,110
90,580
54,180
110,490
43,110
95,930
49,750
65,320
62,970
82,760
66,930
61,130
135,740
58,790
69,170
69,200
124,230
49,700
97,570
57,980
62,790
72,520
71,130
71,500
41,270
78,040
66,150
41,940
74,280
76,530
83,560
126,600
57,230
70,940
140,350
52,070
98,090
71,370
58,680
56,050
83,940
47,300
65,770
108,280
63,230
54,500
46,580
43,310
64,780
49,300
46,410
53,150
95,550
51,740
38,940
56,690
40,210
62,060
58,020
84,860
118,520
85,560
110,620
83,110
59,630
116,150
69,470
78,470
53,780
73,680
48,210
90,570
127,590
72,900
55,980
40,880
56,510
46,310
109,250
60,720
126,840
74,090
53,350
81,860
112,460
134,710
85,870
63,770
71,020
195,620
64,700
102,230
47,350
49,570
49,190
73,270
92,440
78,360
57,600
51,840
63,380
68,290
49,410
64,290
86,420
72,570
121,010
60,500
47,570
61,760
116,310
80,510
65,380
65,010
54,860
66,620
48,440
66,270
48,250
63,760
37,600
47,440
77,540
64,470
67,460
39,480
54,150
56,660
101,950
136,930
63,470
75,270
113,360
65,250
95,750
48,010
50,170
103,040
40,520
77,700
76,810
66,060
56,280
84,210
93,280
111,340
70,780
44,310
69,770
63,330
65,250
63,370
74,180
57,420
94,640
67,560
46,730
63,730
67,260
61,410
42,500
57,790
113,080
64,490
92,970
103,970
70,850
91,980
51,720
75,970
59,080
65,180
60,060
1. Discuss the importance of constructing confidence intervals for the population mean by answering these questio
a. What are confidence intervals?
b. What is a point estimate?
c. What is the best point estimate for the population mean? Explain.
d. Why do we need confidence intervals?
y answering these questions.
2. Using the data from the ‘Data’ tab in this workbook, construct a 95% confidence interval for the population mean.
Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the
confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from Deliverable 1. Do NOT copy and paste the values.
Instead, use cell referencing to use the unrounded values.
Calculate all of the values needed to create this confidence interval to the right.
Below, include a breakdown of the steps, include formulas, and correctly interpret the solution in context of the scenario
with the correct units.
for the population mean.
orrectly interprets the
nd paste the values.
Calculations/Values
Mean
Standard Deviation
n
n in context of the scenario
Critical Value
Margin of Error
Lower Limit
Upper Limit
Formulas/Answers
3. Using the data from the ‘Data’ tab in this workbook, construct a 99% confidence interval for the population mean.
Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the
confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from Deliverable 1. Do NOT copy and paste the values.
Instead, use cell referencing to use the unrounded values.
Calculate all of the values needed to create this confidence interval to the right.
Below, include a breakdown of the steps, include formulas, and correctly interpret the solution in context of the scenario
with the correct units.
or the population mean.
orrectly interprets the
d paste the values.
Calculations/Values
Mean
Standard Deviation
n
in context of the scenario
Critical Value
Margin of Error
Lower Limit
Upper Limit
Formulas/Answers
4. Compare your answers for Question 2 and 3. Notice that the 99% confidence interval is wider.
a. What is the advantage of using a wider confidence interval?
b. Why would you not always use the 99% confidence interval? Explain with an example.
5. We want to estimate the mean salary in Minnesota.
a. How many jobs must be randomly selected for their respective mean salaries if we want 95% confidence that the
sample mean is within $125 of the population mean and σ = $1150.
Show your calculations using Excel functions in the area to the right of this text box and answer the problem with
explanations below.
b. Is the current sample size of 364 in the data set in our Excel workbook large enough? Explain.
95% confidence that the
er the problem with
CV (z)
sigma
E
n