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Confidence Interval Deliverable 3

Develop a confidence interval for a population parameter.

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:

  • A listing of the jobs by title
  • The salary (in dollars) for each job

Deliverable 3 – Confidence Intervals.xlsx

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.

Confidence Interval Deliverable 3 Data

Job TitleSalary
Accountants and Auditors67280source: http://www.bls.gov/
Actuaries100580
Administrative Law Judges, Adjudicators, and Hearing Officers144840Calculations/ValuesFormulas/Answers
Administrative Services Managers97180Mean
Adult Basic and Secondary Education and Literacy Teachers and Instructors63940Standard Deviation
Advertising and Promotions Managers105130n
Advertising Sales Agents51740
Aerospace Engineering and Operations Technicians57140
Aerospace Engineers115220
Agents and Business Managers of Artists, Performers, and Athletes74580
Agricultural and Food Science Technicians40060
Agricultural Inspectors54140
Agricultural Sciences Teachers, Postsecondary87390
Air Traffic Controllers114906
Aircraft Cargo Handling Supervisors50380
Aircraft Structure, Surfaces, Rigging, and Systems Assemblers51410
Airfield Operations Specialists59800
Airline Pilots, Copilots, and Flight Engineers115670
Anthropologists and Archeologists51720
Appraisers and Assessors of Real Estate52870
Arbitrators, Mediators, and Conciliators86430
Architects, Except Landscape and Naval81000
Architectural and Civil Drafters62210
Architecture and Engineering Occupations73850
Architecture Teachers, Postsecondary73870
Archivists76749
Art Directors98924
Art, Drama, and Music Teachers, Postsecondary78700
Athletic Trainers45440
Atmospheric and Space Scientists93900
Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary96590
Audiologists97230
Avionics Technicians47320
Biomedical Engineers101250
Boilermakers76310
Broadcast News Analysts71040
Brokerage Clerks57260
Budget Analysts75940
Business and Financial Operations Occupations64880
Business Operations Specialists, All Other67980
Business Teachers, Postsecondary109800
Buyers and Purchasing Agents, Farm Products62290
Camera and Photographic Equipment Repairers32280
Captains, Mates, and Pilots of Water Vessels63890
Cardiovascular Technologists and Technicians59630
Career/Technical Education Teachers, Middle School69050
Career/Technical Education Teachers, Secondary School63430
Cargo and Freight Agents40910
Cartographers and Photogrammetrists72120
Chefs and Head Cooks47660
Chemical Engineers87200
Chemical Equipment Operators and Tenders45460
Chemical Plant and System Operators54920
Chemical Technicians50360
Chemistry Teachers, Postsecondary96330
Chemists59630
Child, Family, and School Social Workers58140
Chiropractors87540
Civil Engineers91430
Claims Adjusters, Examiners, and Investigators66030
Clinical, Counseling, and School Psychologists76150
Coil Winders, Tapers, and Finishers36610
Commercial and Industrial Designers66710
Commercial Pilots130059
Communications Equipment Operators, All Other43160
Communications Teachers, Postsecondary85310
Community and Social Service Occupations43790
Community Health Workers37190
Compensation and Benefits Managers123570
Compensation, Benefits, and Job Analysis Specialists67210
Compliance Officers67637
Computer and Information Research Scientists121310
Computer and Information Systems Managers137140
Computer and Mathematical Occupations81640
Computer Hardware Engineers95500
Computer Network Architects115050
Computer Network Support Specialists70940
Computer Occupations, All Other92960
Computer Programmers84280
Computer Science Teachers, Postsecondary89290
Computer Systems Analysts90600
Computer User Support Specialists53680
Conservation Scientists67540
Construction and Building Inspectors64150
Construction Managers99150
Continuous Mining Machine Operators55330
Control and Valve Installers and Repairers, Except Mechanical Door64960
Conveyor Operators and Tenders35110
Cost Estimators69480
Crane and Tower Operators53980
Credit Analysts72870
Credit Counselors46720
Criminal Justice and Law Enforcement Teachers, Postsecondary66980
Curators66230
Database Administrators91730
Dental Hygienists71930
Derrick Operators, Oil and Gas38120
Detectives and Criminal Investigators90890
Diagnostic Medical Sonographers74340
Dietitians and Nutritionists60370
Directors, Religious Activities and Education43690
Drafters, All Other51790
Economics Teachers, Postsecondary137920
Economists106280
Editors58820
Education Administrators, All Other79960
Education Administrators, Elementary and Secondary School103570
Education Administrators, Postsecondary110110
Education Administrators, Preschool and Childcare Center/Program81590
Education Teachers, Postsecondary65020
Education, Training, and Library Occupations47920
Educational, Guidance, School, and Vocational Counselors56550
Electric Motor, Power Tool, and Related Repairers63800
Electrical and Electronics Drafters69010
Electrical and Electronics Engineering Technicians68060
Electrical and Electronics Installers and Repairers, Transportation Equipment54060
Electrical and Electronics Repairers, Commercial and Industrial Equipment55970
Electrical and Electronics Repairers, Powerhouse, Substation, and Relay81590
Electrical Engineers91870
Electrical Power-Line Installers and Repairers67430
Electricians60590
Electro-Mechanical Technicians54700
Electronics Engineers, Except Computer100610
Elementary School Teachers, Except Special Education62620
Elevator Installers and Repairers88340
Embalmers48770
Emergency Management Directors79270
Engineering Technicians, Except Drafters, All Other63250
English Language and Literature Teachers, Postsecondary81700
Environmental Engineering Technicians56810
Environmental Engineers84870
Environmental Science and Protection Technicians, Including Health45090
Environmental Science Teachers, Postsecondary92530
Environmental Scientists and Specialists, Including Health84320
Epidemiologists85620
Executive Secretaries and Executive Administrative Assistants55770
Exercise Physiologists54300
Explosives Workers, Ordnance Handling Experts, and Blasters62910
Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders38680
Farm and Home Management Advisors38940
Film and Video Editors62280
Financial Analysts85660
Financial Clerks, All Other44080
Financial Examiners101500
Financial Managers142370
Financial Specialists, All Other87690
Fire Inspectors and Investigators58590
Firefighters49620
First-Line Supervisors of Construction Trades and Extraction Workers82160
First-Line Supervisors of Correctional Officers84290
First-Line Supervisors of Farming, Fishing, and Forestry Workers43150
First-Line Supervisors of Fire Fighting and Prevention Workers91930
First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand49590
First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers54280
First-Line Supervisors of Mechanics, Installers, and Repairers66430
First-Line Supervisors of Non-Retail Sales Workers72920
First-Line Supervisors of Office and Administrative Support Workers58120
First-Line Supervisors of Police and Detectives101240
First-Line Supervisors of Production and Operating Workers60990
First-Line Supervisors of Protective Service Workers, All Other46280
First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators58250
Fish and Game Wardens75430
Food Service Managers51340
Foreign Language and Literature Teachers, Postsecondary73350
Forensic Science Technicians79630
Forest and Conservation Technicians46640
Foresters65970
Forestry and Conservation Science Teachers, Postsecondary90080
Fundraisers57720
Funeral Service Managers82590
Gaming Supervisors32220
Gas Compressor and Gas Pumping Station Operators62720
Gas Plant Operators70130
General and Operations Managers124190
Geography Teachers, Postsecondary82530
Geological and Petroleum Technicians39180
Geoscientists, Except Hydrologists and Geographers70730
Health and Safety Engineers, Except Mining Safety Engineers and Inspectors84880
Health Diagnosing and Treating Practitioners, All Other67650
Health Educators41781
Health Specialties Teachers, Postsecondary136670
Health Technologists and Technicians, All Other45940
Healthcare Practitioners and Technical Occupations67470
Healthcare Social Workers53600
Hearing Aid Specialists46970
Historians84337
History Teachers, Postsecondary88590
Hoist and Winch Operators80,660
Home Economics Teachers, Postsecondary74490
Human Resources Managers112430
Human Resources Specialists61460
Industrial Engineering Technicians55460
Industrial Engineers82720
Industrial Machinery Mechanics55930
Industrial Production Managers100480
Information and Record Clerks, All Other45700
Information Security Analysts97360
Installation, Maintenance, and Repair Occupations45990
Instructional Coordinators66810
Insurance Appraisers, Auto Damage70380
Insurance Sales Agents66080
Insurance Underwriters76990
Interior Designers62010
Judges, Magistrate Judges, and Magistrates58140
Kindergarten Teachers, Except Special Education55850
Labor Relations Specialists51870
Landscape Architects68960
Lawyers140920
Layout Workers, Metal and Plastic42830
Legal Occupations82900
Legal Support Workers, All Other60100
Librarians56320
Library Science Teachers, Postsecondary78830
Life Scientists, All Other82630
Life, Physical, and Social Science Occupations62840
Loading Machine Operators, Underground Mining41270
Loan Officers63040
Locomotive Engineers71960
Logging Workers, All Other41940
Logisticians74600
Magnetic Resonance Imaging Technologists70580
Management Analysts92200
Managers, All Other88600
Marine Engineers and Naval Architects82410
Market Research Analysts and Marketing Specialists62380
Marketing Managers122260
Marriage and Family Therapists55600
Materials Engineers91510
Mathematical Science Teachers, Postsecondary78880
Mechanical Drafters58540
Mechanical Engineering Technicians60220
Mechanical Engineers92040
Media and Communication Equipment Workers, All Other76540
Medical and Clinical Laboratory Technologists65770
Medical and Health Services Managers113030
Medical Equipment Repairers58310
Meeting, Convention, and Event Planners52370
Mental Health Counselors46580
Metal-Refining Furnace Operators and Tenders44990
Middle School Teachers, Except Special and Career/Technical Education66630
Millwrights57190
Mine Cutting and Channeling Machine Operators46250
Mine Shuttle Car Operators56930
Mining and Geological Engineers, Including Mining Safety Engineers93920
Mining Machine Operators, All Other69160
Mixing and Blending Machine Setters, Operators, and Tenders41970
Mobile Heavy Equipment Mechanics, Except Engines58950
Model Makers, Metal and Plastic57100
Morticians, Undertakers, and Funeral Directors69800
Multimedia Artists and Animators59890
Music Directors and Composers46260
Natural Sciences Managers113620
Network and Computer Systems Administrators87700
Nuclear Engineers121650
Nuclear Medicine Technologists79440
Nuclear Technicians88770
Nurse Practitioners101960
Nursing Instructors and Teachers, Postsecondary72450
Occupational Health and Safety Specialists75610
Occupational Health and Safety Technicians61740
Occupational Therapists82290
Occupational Therapy Assistants61860
Operations Research Analysts90310
Optometrists111790
Orthotists and Prosthetists82380
Painters, Transportation Equipment45230
Paper Goods Machine Setters, Operators, and Tenders37110
Paralegals and Legal Assistants56990
Patternmakers, Metal and Plastic56260
Personal Financial Advisors121750
Petroleum Pump System Operators, Refinery Operators, and Gaugers66550
Pharmacists120280
Philosophy and Religion Teachers, Postsecondary78010
Physical Therapist Assistants58720
Physical Therapists90040
Physician Assistants104730
Physicists118520
Physics Teachers, Postsecondary89040
Plant and System Operators, All Other56830
Plumbers, Pipefitters, and Steamfitters77570
Podiatrists195730
Police and Sheriff’s Patrol Officers74870
Political Science Teachers, Postsecondary90250
Postal Service Clerks49310
Postal Service Mail Carriers50160
Postal Service Mail Sorters, Processors, and Processing Machine Operators49820
Postmasters and Mail Superintendents75620
Power Distributors and Dispatchers84830
Power Plant Operators79100
Precision Instrument and Equipment Repairers, All Other64170
Private Detectives and Investigators58290
Probation Officers and Correctional Treatment Specialists64300
Producers and Directors75970
Production, Planning, and Expediting Clerks48390
Property, Real Estate, and Community Association Managers66710
Psychologists, All Other79010
Psychology Teachers, Postsecondary89680
Public Relations and Fundraising Managers115180
Public Relations Specialists63620
Pump Operators, Except Wellhead Pumpers51520
Purchasing Agents, Except Wholesale, Retail, and Farm Products61760
Purchasing Managers111380
Radiation Therapists84640
Radio, Cellular, and Tower Equipment Installers and Repairers49240
Radiologic Technologists63420
Rail Yard Engineers, Dinkey Operators, and Hostlers54790
Railroad Conductors and Yardmasters65740
Rail-Track Laying and Maintenance Equipment Operators54600
Real Estate Brokers88750
Real Estate Sales Agents59010
Recreation and Fitness Studies Teachers, Postsecondary60080
Recreational Vehicle Service Technicians34450
Refractory Materials Repairers, Except Brickmasons49210
Registered Nurses71730
Reinforcing Iron and Rebar Workers86290
Respiratory Therapists56910
Rolling Machine Setters, Operators, and Tenders, Metal and Plastic38060
Roof Bolters, Mining58900
Rotary Drill Operators, Oil and Gas49720
Sales Engineers98760
Sales Managers75432
Sales Representatives, Services, All Other61930
Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products69900
Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products81950
Secondary School Teachers, Except Special and Career/Technical Education68380
Securities, Commodities, and Financial Services Sales Agents86070
Service Unit Operators, Oil, Gas, and Mining42200
Set and Exhibit Designers54620
Ship Engineers57066
Signal and Track Switch Repairers38120
Social and Community Service Managers63870
Social Scientists and Related Workers, All Other79960
Social Work Teachers, Postsecondary54580
Social Workers, All Other65890
Sociology Teachers, Postsecondary87710
Software Developers, Applications96110
Software Developers, Systems Software106700
Soil and Plant Scientists57080
Sound Engineering Technicians58660
Special Education Teachers, All Other59400
Special Education Teachers, Kindergarten and Elementary School65430
Special Education Teachers, Middle School62160
Special Education Teachers, Secondary School68560
Speech-Language Pathologists78760
Stationary Engineers and Boiler Operators79090
Statisticians88190
Surveyors60215
Tank Car, Truck, and Ship Loaders45470
Tax Examiners and Collectors, and Revenue Agents79850
Technical Writers67410
Telecommunications Equipment Installers and Repairers, Except Line Installers57580
Tire Builders42500
Tool and Die Makers54680
Training and Development Managers101500
Training and Development Specialists59910
Transportation Inspectors86790
Transportation, Storage, and Distribution Managers93250
Urban and Regional Planners79510
Veterinarians93830
Water and Wastewater Treatment Plant and System Operators54560
Web Developers57450
Wholesale and Retail Buyers, Except Farm Products55080
Writers and Authors53050
Zoologists and Wildlife Biologists62420

Confidence Interval Deliverable 3 Question 1

  1. Discuss the importance of constructing confidence intervals for the population mean by answering these questions. 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?

Confidence Interval Deliverable 3 Question 2

Calculations/ValuesFormulas/Answers
Mean
Standard Deviation
n
Critical Value
Margin of Error
Lower Limit
Upper Limit
  1. 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.

Confidence Interval Question 3

Calculations/ValuesFormulas/Answers
Mean
Standard Deviation
n
Critical Value
Margin of Error
Lower Limit
Upper Limit
  1. 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.

Confidence Interval Question 4

  1. 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.

Confidence Interval Deliverable 3 Question 5

CV (z)
sigma
E
n
  1. 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 $130 of the population mean and σ = $1240. 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.

Last Updated on June 14, 2022

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