1) Discuss the importance of constructing confidence intervals for the populatio
ID: 3243825 • Letter: 1
Question
1) Discuss the importance of constructing confidence intervals for the population mean by answering these questions.
What are confidence intervals?
What is a point estimate?
What is the best point estimate for the population mean? Explain.
Why do we need confidence intervals?
2) Evaluate the following:
Find the best point estimate of the population mean.
Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.
3) We want to estimate the mean salary in Minnesota. Is the sample size of the data set, 364, sufficiently large? Explain. Assume that we want 95% confidence that the sample mean is within $1150 of the population mean and = $126.
Spreadsheet below:
Job Title Salary Accountants and Auditors 40,170 Actuaries 40,170 Administrative Law Judges, Adjudicators, and Hearing Officers 40,300 Administrative Services Managers 40,310 Adult Basic and Secondary Education and Literacy Teachers and Instructors 40,400 Advertising and Promotions Managers 40,580 Advertising Sales Agents 40,590 Aerospace Engineering and Operations Technicians 40,590 Aerospace Engineers 40,600 Agents and Business Managers of Artists, Performers, and Athletes 40,740 Agricultural and Food Science Technicians 41,040 Agricultural Inspectors 41,050 Agricultural Sciences Teachers, Postsecondary 41,180 Air Traffic Controllers 41,190 Aircraft Cargo Handling Supervisors 41,230 Aircraft Structure, Surfaces, Rigging, and Systems Assemblers 41,270 Airfield Operations Specialists 41,290 Airline Pilots, Copilots, and Flight Engineers 41,360 Anthropologists and Archeologists 41,380 Appraisers and Assessors of Real Estate 41,400 Arbitrators, Mediators, and Conciliators 41,470 Architects, Except Landscape and Naval 41,590 Architectural and Civil Drafters 41,700 Architecture and Engineering Occupations 41,780 Architecture Teachers, Postsecondary 41,850 Archivists 41,870 Art Directors 41,910 Art, Drama, and Music Teachers, Postsecondary 41,940 Athletic Trainers 42,170 Atmospheric and Space Scientists 42,230 Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary 42,330 Audiologists 42,340 Avionics Technicians 42,410 Biomedical Engineers 42,490 Boilermakers 42,500 Broadcast News Analysts 42,510 Brokerage Clerks 42,720 Budget Analysts 42,750 Business and Financial Operations Occupations 42,760 Business Operations Specialists, All Other 42,830 Business Teachers, Postsecondary 43,000 Buyers and Purchasing Agents, Farm Products 43,140 Camera and Photographic Equipment Repairers 43,150 Captains, Mates, and Pilots of Water Vessels 43,200 Cardiovascular Technologists and Technicians 43,210 Career/Technical Education Teachers, Middle School 43,260 Career/Technical Education Teachers, Secondary School 43,300 Cargo and Freight Agents 43,340 Cartographers and Photogrammetrists 43,360 Chefs and Head Cooks 43,370 Chemical Engineers 43,470 Chemical Equipment Operators and Tenders 43,500 Chemical Plant and System Operators 43,690 Chemical Technicians 43,780 Chemistry Teachers, Postsecondary 43,910 Chemists 43,940 Child, Family, and School Social Workers 43,970 Chiropractors 44,080 Civil Engineers 44,240 Claims Adjusters, Examiners, and Investigators 44,310 Clinical, Counseling, and School Psychologists 44,330 Coil Winders, Tapers, and Finishers 44,470 Commercial and Industrial Designers 44,570 Commercial Pilots 44,610 Communications Equipment Operators, All Other 44,690 Communications Teachers, Postsecondary 44,890 Community and Social Service Occupations 44,920 Community Health Workers 45,000 Compensation and Benefits Managers 45,020 Compensation, Benefits, and Job Analysis Specialists 45,090 Compliance Officers 45,150 Computer and Information Research Scientists 45,400 Computer and Information Systems Managers 45,460 Computer and Mathematical Occupations 45,510 Computer Hardware Engineers 45,510 Computer Network Architects 45,610 Computer Network Support Specialists 45,660 Computer Occupations, All Other 46,020 Computer Programmers 46,100 Computer Science Teachers, Postsecondary 46,100 Computer Systems Analysts 46,110 Computer User Support Specialists 46,170 Conservation Scientists 46,200 Construction and Building Inspectors 46,320 Construction Managers 46,410 Continuous Mining Machine Operators 46,470 Control and Valve Installers and Repairers, Except Mechanical Door 46,530 Conveyor Operators and Tenders 46,540 Cost Estimators 46,720 Crane and Tower Operators 46,730 Credit Analysts 46,750 Credit Counselors 46,760 Criminal Justice and Law Enforcement Teachers, Postsecondary 46,990 Curators 47,070 Database Administrators 47,100 Dental Hygienists 47,290 Derrick Operators, Oil and Gas 47,440 Detectives and Criminal Investigators 47,760 Diagnostic Medical Sonographers 47,990 Dietitians and Nutritionists 48,010 Directors, Religious Activities and Education 48,090 Drafters, All Other 48,120 Economics Teachers, Postsecondary 48,190 Economists 48,230 Editors 48,260 Education Administrators, All Other 48,360 Education Administrators, Elementary and Secondary School 48,470 Education Administrators, Postsecondary 48,520 Education Administrators, Preschool and Childcare Center/Program 48,790 Education Teachers, Postsecondary 48,810 Education, Training, and Library Occupations 48,830 Educational, Guidance, School, and Vocational Counselors 48,970 Electric Motor, Power Tool, and Related Repairers 49,150 Electrical and Electronics Drafters 49,350 Electrical and Electronics Engineering Technicians 49,430 Electrical and Electronics Installers and Repairers, Transportation Equipment 49,580 Electrical and Electronics Repairers, Commercial and Industrial Equipment 49,580 Electrical and Electronics Repairers, Powerhouse, Substation, and Relay 49,620 Electrical Engineers 49,630 Electrical Power-Line Installers and Repairers 49,740 Electricians 50,100 Electro-Mechanical Technicians 50,150 Electronics Engineers, Except Computer 50,170 Elementary School Teachers, Except Special Education 50,290 Elevator Installers and Repairers 50,610 Embalmers 50,810 Emergency Management Directors 50,820 Engineering Technicians, Except Drafters, All Other 50,920 English Language and Literature Teachers, Postsecondary 50,940 Environmental Engineering Technicians 51,410 Environmental Engineers 51,570 Environmental Science and Protection Technicians, Including Health 51,900 Environmental Science Teachers, Postsecondary 51,930 Environmental Scientists and Specialists, Including Health 52,200 Epidemiologists 52,200 Executive Secretaries and Executive Administrative Assistants 52,330 Exercise Physiologists 52,330 Explosives Workers, Ordnance Handling Experts, and Blasters 52,340 Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders 52,340 Farm and Home Management Advisors 52,390 Film and Video Editors 52,430 Financial Analysts 52,450 Financial Clerks, All Other 52,530 Financial Examiners 52,650 Financial Managers 52,710 Financial Specialists, All Other 52,740 Fire Inspectors and Investigators 52,840 Firefighters 52,900 First-Line Supervisors of Construction Trades and Extraction Workers 52,950 First-Line Supervisors of Correctional Officers 53,150 First-Line Supervisors of Farming, Fishing, and Forestry Workers 53,190 First-Line Supervisors of Fire Fighting and Prevention Workers 53,210 First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand 53,470 First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers 53,480 First-Line Supervisors of Mechanics, Installers, and Repairers 53,710 First-Line Supervisors of Non-Retail Sales Workers 53,830 First-Line Supervisors of Office and Administrative Support Workers 53,860 First-Line Supervisors of Police and Detectives 54,050 First-Line Supervisors of Production and Operating Workers 54,140 First-Line Supervisors of Protective Service Workers, All Other 54,150 First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators 54,170 Fish and Game Wardens 54,250 Food Service Managers 54,330 Foreign Language and Literature Teachers, Postsecondary 54,620 Forensic Science Technicians 55,190 Forest and Conservation Technicians 55,310 Foresters 55,340 Forestry and Conservation Science Teachers, Postsecondary 55,430 Fundraisers 55,510 Funeral Service Managers 55,630 Gaming Supervisors 55,700 Gas Compressor and Gas Pumping Station Operators 55,820 Gas Plant Operators 55,870 General and Operations Managers 55,870 Geography Teachers, Postsecondary 55,900 Geological and Petroleum Technicians 55,990 Geoscientists, Except Hydrologists and Geographers 55,990 Health and Safety Engineers, Except Mining Safety Engineers and Inspectors 56,020 Health Diagnosing and Treating Practitioners, All Other 56,050 Health Educators 56,160 Health Specialties Teachers, Postsecondary 56,220 Health Technologists and Technicians, All Other 56,440 Healthcare Practitioners and Technical Occupations 56,600 Healthcare Social Workers 56,600 Hearing Aid Specialists 56,700 Historians 56,980 History Teachers, Postsecondary 56,990 Hoist and Winch Operators 57,160 Home Economics Teachers, Postsecondary 57,180 Human Resources Managers 57,210 Human Resources Specialists 57,230 Industrial Engineering Technicians 57,230 Industrial Engineers 57,390 Industrial Machinery Mechanics 57,510 Industrial Production Managers 57,620 Information and Record Clerks, All Other 57,700 Information Security Analysts 57,820 Installation, Maintenance, and Repair Occupations 58,140 Instructional Coordinators 58,160 Insurance Appraisers, Auto Damage 58,210 Insurance Sales Agents 58,340 Insurance Underwriters 58,420 Interior Designers 58,590 Judges, Magistrate Judges, and Magistrates 58,640 Kindergarten Teachers, Except Special Education 58,700 Labor Relations Specialists 58,870 Landscape Architects 59,000 Lawyers 59,010 Layout Workers, Metal and Plastic 59,130 Legal Occupations 59,590 Legal Support Workers, All Other 59,630 Librarians 59,730 Library Science Teachers, Postsecondary 59,760 Life Scientists, All Other 59,800 Life, Physical, and Social Science Occupations 59,820 Loading Machine Operators, Underground Mining 60,040 Loan Officers 60,360 Locomotive Engineers 60,470 Logging Workers, All Other 60,560 Logisticians 60,720 Magnetic Resonance Imaging Technologists 61,290 Management Analysts 61,300 Managers, All Other 61,360 Marine Engineers and Naval Architects 61,440 Market Research Analysts and Marketing Specialists 61,760 Marketing Managers 61,780 Marriage and Family Therapists 62,210 Materials Engineers 62,320 Mathematical Science Teachers, Postsecondary 62,600 Mechanical Drafters 62,630 Mechanical Engineering Technicians 62,740 Mechanical Engineers 62,800 Media and Communication Equipment Workers, All Other 63,080 Medical and Clinical Laboratory Technologists 63,400 Medical and Health Services Managers 63,490 Medical Equipment Repairers 63,870 Meeting, Convention, and Event Planners 63,910 Mental Health Counselors 63,950 Metal-Refining Furnace Operators and Tenders 64,250 Middle School Teachers, Except Special and Career/Technical Education 65,060 Millwrights 65,140 Mine Cutting and Channeling Machine Operators 65,650 Mine Shuttle Car Operators 66,150 Mining and Geological Engineers, Including Mining Safety Engineers 66,370 Mining Machine Operators, All Other 66,490 Mixing and Blending Machine Setters, Operators, and Tenders 66,660 Mobile Heavy Equipment Mechanics, Except Engines 66,890 Model Makers, Metal and Plastic 67,040 Morticians, Undertakers, and Funeral Directors 67,070 Multimedia Artists and Animators 67,390 Music Directors and Composers 67,430 Natural Sciences Managers 67,440 Network and Computer Systems Administrators 67,910 Nuclear Engineers 67,930 Nuclear Medicine Technologists 67,970 Nuclear Technicians 68,470 Nurse Practitioners 68,750 Nursing Instructors and Teachers, Postsecondary 68,910 Occupational Health and Safety Specialists 68,990 Occupational Health and Safety Technicians 69,080 Occupational Therapists 69,300 Occupational Therapy Assistants 69,970 Operations Research Analysts 70,120 Optometrists 70,520 Orthotists and Prosthetists 70,530 Painters, Transportation Equipment 70,740 Paper Goods Machine Setters, Operators, and Tenders 71,100 Paralegals and Legal Assistants 71,260 Patternmakers, Metal and Plastic 71,400 Personal Financial Advisors 71,420 Petroleum Pump System Operators, Refinery Operators, and Gaugers 71,890 Pharmacists 72,760 Philosophy and Religion Teachers, Postsecondary 73,260 Physical Therapist Assistants 73,650 Physical Therapists 73,780 Physician Assistants 74,600 Physicists 75,440 Physics Teachers, Postsecondary 75,530 Plant and System Operators, All Other 75,710 Plumbers, Pipefitters, and Steamfitters 76,280 Podiatrists 77,280 Police and Sheriff's Patrol Officers 77,690 Political Science Teachers, Postsecondary 77,880 Postal Service Clerks 78,040 Postal Service Mail Carriers 78,240 Postal Service Mail Sorters, Processors, and Processing Machine Operators 78,630 Postmasters and Mail Superintendents 78,700 Power Distributors and Dispatchers 78,810 Power Plant Operators 79,040 Precision Instrument and Equipment Repairers, All Other 79,200 Private Detectives and Investigators 79,450 Probation Officers and Correctional Treatment Specialists 79,820 Producers and Directors 79,910 Production, Planning, and Expediting Clerks 80,010 Property, Real Estate, and Community Association Managers 80,490 Psychologists, All Other 80,690 Psychology Teachers, Postsecondary 81,140 Public Relations and Fundraising Managers 81,280 Public Relations Specialists 81,330 Pump Operators, Except Wellhead Pumpers 81,870 Purchasing Agents, Except Wholesale, Retail, and Farm Products 81,970 Purchasing Managers 82,560 Radiation Therapists 83,170 Radio, Cellular, and Tower Equipment Installers and Repairers 83,370 Radiologic Technologists 83,460 Rail Yard Engineers, Dinkey Operators, and Hostlers 83,940 Railroad Conductors and Yardmasters 84,190 Rail-Track Laying and Maintenance Equipment Operators 84,390 Real Estate Brokers 84,830 Real Estate Sales Agents 85,800 Recreation and Fitness Studies Teachers, Postsecondary 85,810 Recreational Vehicle Service Technicians 86,080 Refractory Materials Repairers, Except Brickmasons 86,090 Registered Nurses 87,210 Reinforcing Iron and Rebar Workers 87,630 Respiratory Therapists 87,680 Rolling Machine Setters, Operators, and Tenders, Metal and Plastic 88,320 Roof Bolters, Mining 88,400 Rotary Drill Operators, Oil and Gas 88,670 Sales Engineers 88,680 Sales Managers 89,080 Sales Representatives, Services, All Other 89,680 Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products 90,080 Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products 90,310 Secondary School Teachers, Except Special and Career/Technical Education 91,040 Securities, Commodities, and Financial Services Sales Agents 91,070 Service Unit Operators, Oil, Gas, and Mining 91,360 Set and Exhibit Designers 92,010 Ship Engineers 92,420 Signal and Track Switch Repairers 92,630 Social and Community Service Managers 93,500 Social Scientists and Related Workers, All Other 93,630 Social Work Teachers, Postsecondary 93,750 Social Workers, All Other 93,970 Sociology Teachers, Postsecondary 94,030 Software Developers, Applications 94,450 Software Developers, Systems Software 94,950 Soil and Plant Scientists 95,030 Sound Engineering Technicians 95,040 Special Education Teachers, All Other 96,210 Special Education Teachers, Kindergarten and Elementary School 96,290 Special Education Teachers, Middle School 96,290 Special Education Teachers, Secondary School 98,480 Speech-Language Pathologists 99,260 Stationary Engineers and Boiler Operators 99,980 Statisticians 100,310 Surveyors 101,700 Tank Car, Truck, and Ship Loaders 103,900 Tax Examiners and Collectors, and Revenue Agents 104,280 Technical Writers 104,300 Telecommunications Equipment Installers and Repairers, Except Line Installers 104,730 Tire Builders 106,790 Tool and Die Makers 108,160 Training and Development Managers 108,740 Training and Development Specialists 110,620 Transportation Inspectors 111,320 Transportation, Storage, and Distribution Managers 111,910 Urban and Regional Planners 112,230 Veterinarians 113,650 Water and Wastewater Treatment Plant and System Operators 116,110 Web Developers 117,110 Wholesale and Retail Buyers, Except Farm Products 119,020 Writers and Authors 119,170 Zoologists and Wildlife Biologists 119,850Explanation / Answer
1)An interval I(x) which is a subset of , is said to constitute a confidence interval of with confidence coefficient (1-) if,
P[ € I(x)] = 1-, for all € .
Estimation of a parameter by a single value or point T(x) is referred to as point estimaton.
The best point estimate for the population mean is the sample mean, since the sample mean is an unbiased estimator of population mean.
A confidence interval is a range of values, derived from sample statistic that is likely to contain the value of an unknown population parameter. The confidence interval represents the accuracy or precision of an estimate.
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