Confidence Intervals

User Generated

xnlyrluneevf

Business Finance

Rasmussen University

Description

Given a real-life application, develop a confidence interval for a population parameter and its interpretation. 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 jobYou 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. Your research and analysis should be present within the answers provided on the worksheet.

Unformatted Attachment Preview

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 70500 102880 117190 96180 63940 104130 51740 56140 115220 74580 42060 54140 87390 124540 52480 51410 59800 115670 57720 52870 86430 81000 62210 73850 73870 60730 92680 78700 45440 93900 96590 97230 47320 99000 76310 71040 57260 75940 64880 67980 119810 62290 32280 63890 59630 69050 source: http://www.bls.gov/ 63430 40910 72120 47660 87200 45460 54920 50360 96330 76620 58140 86820 91430 66030 76150 36610 66710 104420 43160 85310 43790 37190 121570 67210 71780 121310 137140 81640 95500 112050 70940 92960 84280 89290 90600 53680 67540 64150 99150 55330 64960 35110 69480 53980 72870 46720 66980 66230 91730 71930 38120 90890 74340 60370 43690 51790 137920 106280 58820 79960 103570 110110 65860 65020 47920 56550 63800 69010 68060 54060 55970 81590 91870 67430 74010 54700 100610 62620 88340 48770 79270 63250 81700 56810 84870 45090 92530 84320 85620 55770 54300 62910 38680 38940 62280 85660 44080 99800 134370 87690 58590 49620 82160 84290 42540 91930 49590 54280 66430 72920 58120 101240 60990 46280 58250 88120 51340 73350 79630 46640 65970 90080 57720 82590 32220 62720 70130 124190 82530 39180 70730 84880 67650 58050 136670 45940 67470 53600 46970 70840 88590 80,660 74490 112430 61460 55460 82720 55930 100480 45700 97360 45990 66810 70380 66080 76990 62010 58140 55850 51870 68960 140920 42830 82900 59800 56320 78830 82630 62840 41270 63040 71960 41940 74600 70580 92200 88600 82410 62380 122260 55600 91510 78880 58540 60220 92040 76540 65770 113030 58310 52370 46580 44990 66630 58660 46250 56930 93920 69160 41970 58950 57100 69800 59890 46260 113620 87700 121650 79440 88770 101960 72450 75610 61740 82290 61860 90310 111790 82380 45230 37110 56990 56260 121750 66550 120280 78010 57750 90040 104730 118520 89040 56830 77570 192180 73870 90250 49310 50160 49820 75620 84830 79100 64170 58290 64300 75970 48390 66710 79010 89680 115180 63620 51520 61760 111380 84640 49240 63100 54790 65740 54600 86260 59010 60080 34450 49210 71730 86290 56910 38060 58900 49720 98760 128340 61930 69900 81950 68380 86070 42200 54620 69300 37720 63870 79960 54580 65890 87710 96110 106700 57080 58660 59400 65430 62160 68560 78760 79090 88190 62580 45470 79850 67410 57580 42500 54680 101500 59910 86790 92220 79510 93830 54560 69430 59080 62170 63420 Deliverable 03 Worksheet 1. Discuss the importance of constructing confidence intervals for the population mean by answering these questions. o What are confidence intervals? o What is a point estimate? o What is the best point estimate for the population mean? Explain. o Why do we need confidence intervals? Answer and Explanation: Enter your step-by-step answer and explanations here. 2. Using the data from the Excel 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. Answer and Explanation: Enter your step-by-step answer and explanations here. 3. Using the data from the Excel 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. Answer and Explanation: Enter your step-by-step answer and explanations here. 4. Compare your answers for (2) and (3). You notice that the 99% confidence interval is wider. What is the advantage of using a wider confidence interval? Why would you not always use the 99% confidence interval? Explain with an example. Answer and Explanation: Enter your step-by-step answer and explanations here. 5. We want to estimate the mean salary in Minnesota. How many jobs must be randomly selected for their respective mean salaries if we want 95% confidence that the sample mean is within $126 of the population mean and σ = $1150. Is the current sample size of 364 in the data set in our Excel workbook large enough? Explain. Answer and Explanation: Enter your step-by-step answer and explanations here.
Purchase answer to see full attachment
Explanation & Answer:
5 Questions
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Here it is :)

Deliverable 03 Worksheet
1. Discuss the importance of constructing confidence intervals for the population mean by
answering these questions.
o
o
o
o

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?

Answer and Explanation:
A confidence interval gives the probability that the mean of a population
will fall between a range estimated using a sample of the population. A
point estimate is a value used to estimate a population parameter. The
best point estimate for the population mean is the sample mean because a
good sample should be a representation of the population. We need
confidence intervals because it may not be realistic to gather information
on an entire population.

2. Using the data from the Excel 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.
Answer and Explanation:

Sample mean
Sample S
n
df
Confidence
Alpha

72224.34
22644.46
364
363
0.95
0.05

Because the standard deviation for the population is unknown, we can calculate
𝑠

the error for the confidence interval using the formula (𝑡𝑠𝑡𝑎𝑡) ( 𝑛). The t-stat is


calculated using a table in which alpha is .05 and the degrees freedom is 363.
The t-stat in this case is 1.966521
The error in this case can be found by substituting in the information
22644.46

1.966521 (

√364

) =2334.05. Once you find the error, add and subtract the error

from the sample mean to estimate the population mean with 95% probability.
The confidence interval is 69890.29≤ 𝜇 ≤74558.39
There is a 95% probability that the population mean of salaries is between 69,890.29
and 74,558.39.

3. Using the data from the Excel 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.
Answer and Explanation:

Sample mean
Sample S
n
df
Confidence
Alpha

72224.34
22644.46
364
363
0.99
0.01

Because the standard deviation for the population is unknown, we can
𝑠

calculate the error for the confidence interval using the formula (𝑡𝑠𝑡𝑎𝑡) ( 𝑛).


The t-stat is calculated using a table in which alpha is .01 and the degrees
freedom is 363. The t-stat in this case is 2.589441
The error in this case can be found by substituting in the information
22644.46

2.589441 (

√364

) = 3073.39. Once you find the error, add and subtract the error

from the sample mean to estimate the population mean with 99% probability.
The confidence interval is 69150.95≤ 𝜇 ≤ 75297.73
There is a 99% probability that the population mean of salaries is between 69150.95
and 75297.73.

4. Compare your answers for (2) and (3). You notice that the 99% confidence interval
is wider. What is the advantage of using a wider confidence interval? Why would
you not always use the 99% confidence interval? Explain with an example.
Answer and Explanation:

The advantage of using a wider confidence interval is having a higher
probability of estimating the population mean because 99% of salaries
should fall within that range. By increasing your confidence interval, you are
actually increasing the error. Sometimes you can increase an interval so
much that it will be useless to use. For example, if our confidence interval
for the mean of the number of siblings a population has is 1 to 20, it doesn’t
narrow down the mean of the population very well. You have a higher
chance of being accurate because the range of values is larger, but the data
varies so much that it is not very helpful.
5. We want to estimate the mean salary in Minnesota. How many jobs must be
randomly selected for their respective mean salaries if we want 95% confidence
that the sample mean is within $126 of t...


Anonymous
Really great stuff, couldn't ask for more.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags