Inferential Statistics

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Unzorna19

Business Finance

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Chose- Option 1 (Minnesota)- Have attached the Excel spreadsheet with the information, I have also attached the papers I have wrote the past 2 weeks. Please let me know if you have any further questions.


This week you will begin working on Phase 4 of your course project. For Phase 4 of your course project, you will want to review your instructor's feedback from your Phase 1, Phase 2, and Phase 3 submissions to make any necessary corrections. Remember if you have questions about the feedback to ask your instructor for assistance.

Once you have made your corrections, you will compile your information from Phase 1, Phase 2, Phase 3 and your final conclusion into one submission and submit this as your rough draft for Phase 4 of the course project. Below is a summary of the expectations for Phase 4 of the course project:

  1. Introduce your scenario and data set.
    • Provide a brief overview of the scenario you are given above and the data set that you will be analyzing.
    • Classify the variables in your data set.
      • Which variables are quantitative/qualitative?
      • Which variables are discrete/continuous?
      • Describe the level of measurement for each variable included in your data set.
  1. Discuss the importance of the Measures of Center and the Measures of Variation.
    • What are the measures of center and why are they important?
    • What are the measures of variation and why are they important?
  1. Calculate the measures of center and measures of variation. Interpret your results in context of the selected topic.
    • Mean
    • Median
    • Mode
    • Midrange
    • Range
    • Variance
    • Standard Deviantion
  1. Discuss the importance of constructing confidence intervals for the population mean.
    • 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?
  1. Based on your selected topic, 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 σ is unknown.
      • Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
    • Write a statement that correctly interprets the confidence interval in context of your selected topic.
  1. Based on your selected topic, evaluate the following:
    • Find the best point estimate of the population mean.
    • Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown.
      • Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.
    • Write a statement that correctly interprets the confidence interval in context of your selected topic.
  1. Compare and contrast your findings for the 95% and 99% confidence interval.
    • Did you notice any changes in your interval estimate? Explain.
    • What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.
  1. Discuss the process for hypothesis testing.
    • Discuss the 8 steps of hypothesis testing?
    • When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value method or Critical Value method? Why?
  1. Perform the hypothesis test.
    • If you selected Option 1:
      • Original Claim: The average salary for all jobs in Minnesota is less than $65,000.
      • Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown.
    • If you selected Option 2:
      • Original Claim: The average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age.
      • Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown.
    • Based on your selected topic, answer the following:
      1. Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim.
      2. Is the test two-tailed, left-tailed, or right-tailed? Explain.
      3. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain.
      4. What is the value of the test-statistic? What is the P-value? What is the critical value?
      5. 5.) What is your decision; reject the null or do not reject the null?
        1. Explain why you made your decision including the results for your p-value and the critical value.
      6. State the final conclusion in non-technical terms.
  1. Conclusion
    • Recap your ideas by summarizing the information presented in context of your chosen scenario.

Please be sure to show all of your work and use the Equation Editor to format your equations.

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 63,910 84,190 117,110 94,450 43,500 75,710 46,100 59,800 104,730 77,690 44,470 43,470 92,010 94,030 44,890 42,410 52,740 98,480 43,970 50,150 56,700 75,440 46,470 79,910 79,040 60,560 76,280 57,210 42,330 84,390 92,630 53,830 56,440 85,810 55,870 84,830 43,690 73,650 66,890 77,280 78,240 63,490 41,910 69,080 44,690 53,190 source: http://www.bls.gov/ 53,480 45,610 54,170 45,090 92,420 52,430 52,710 43,370 71,100 70,740 40,580 80,690 71,890 58,870 85,800 48,260 48,120 83,940 40,600 64,250 41,400 42,490 87,210 56,600 62,600 103,900 119,170 73,780 99,980 88,400 55,990 83,170 80,490 91,360 79,200 45,150 71,400 49,630 89,680 42,760 41,050 40,400 56,980 43,910 50,290 43,360 57,230 48,470 70,120 46,530 44,610 57,820 47,760 46,720 41,590 48,090 96,290 104,280 46,760 81,870 77,880 95,040 61,290 57,390 45,000 50,820 41,380 61,360 56,160 52,450 52,650 63,870 91,040 59,730 43,200 49,150 100,310 48,970 67,930 46,100 67,970 62,320 52,330 48,520 69,970 42,510 78,700 58,640 59,130 52,530 43,150 49,580 41,190 49,430 43,940 93,970 42,830 78,040 116,110 67,910 47,100 40,590 55,990 53,470 46,170 57,160 44,310 40,300 59,010 74,600 49,740 62,800 55,630 44,570 52,950 46,110 59,820 55,340 41,700 43,210 56,020 90,080 51,930 53,210 43,260 56,220 61,780 119,850 67,430 58,700 71,260 88,670 56,990 44,920 108,160 43,140 63,080 44,080 42,170 62,210 56,050 54,330 71,420 93,630 58,160 57,510 81,330 48,790 93,500 41,230 78,810 42,340 65,060 75,530 54,050 52,330 46,540 58,140 47,990 50,100 72,760 106,790 47,290 81,140 51,570 52,340 60,360 55,510 58,420 41,270 67,070 55,900 41,940 81,280 55,430 90,310 94,950 57,230 58,340 111,320 43,780 95,030 62,740 52,840 51,900 83,370 66,370 52,900 93,750 44,240 45,020 42,720 44,330 48,830 43,300 46,410 53,150 81,970 45,660 40,740 43,340 41,780 40,170 57,700 48,190 113,650 68,990 110,620 55,820 59,630 88,320 66,660 66,150 49,620 73,260 55,190 87,680 96,210 62,630 41,180 41,360 45,510 40,310 101,700 54,140 119,020 61,760 53,710 83,460 88,680 108,740 78,630 67,440 40,170 112,230 41,040 66,490 45,400 49,350 48,360 68,750 70,530 60,720 46,990 57,620 43,000 50,920 46,020 67,390 86,080 68,910 89,080 47,070 41,850 63,950 104,300 68,470 45,510 45,460 49,580 52,200 46,320 70,520 56,600 61,300 42,230 47,440 55,870 40,590 46,200 41,290 54,150 41,470 99,260 111,910 48,230 63,400 79,450 50,170 82,560 48,010 54,620 69,300 52,340 61,440 80,010 67,040 60,040 59,760 91,070 96,290 60,470 41,870 55,310 50,810 52,200 52,390 65,140 46,730 58,210 51,410 48,810 53,860 59,590 50,940 42,500 46,750 87,630 57,180 65,650 86,090 58,590 79,820 42,750 50,610 55,700 54,250 59,000 Course Project: Phase 2 Confidence Intervals In this part of the project we will be focusing on confidence intervals. We will be finding out what they are. We will also learn how to work out the right answers and use tables to find those answers with the information provided. In this case we will be working with the excel spreadsheet with information on Minnesota salary wages. Confidence Intervals What are confidence intervals? Confidence intervals are a range or an interval of values that are used to estimate the true value of a population parameter. “A confidence interval is sometimes abbreviated as CI (Triola, 2014).” When dealing with confidence intervals you will also run into the term, point estimate. A point estimate is a single value that is used to estimate a population parameter. The best point estimate for the population means that the mean you get from a sample calculates the average. The reason for this is that the sample of the mean has the characteristics of being the unbiased estimate of the mean population. Why do we need confidence intervals? We need confidence intervals because it’s considered the size of your samples and the variations. They give you an idea on how accurate your estimate will be. A confidence level is a range of likely values that p might take. The width of the confidence interval is related to the confidence level desired. The higher the percentage of confidence desired, the wider the confidence interval. Examples from the Excel Spreadsheet Data The best point estimate of the population mean from the wages presented from the Excel spreadsheet and provided by the Bureau of Labor Statistics, would be $62306.13. Now let’s explore confidence levels with certain scenarios presented from the date: Construct two confidence intervals for the population mean: a 95% confidence interval and a 99% confidence interval. Assume that your data is normally distributed and the population standard deviation is unknown. Let’s find the margin of error  s 2 n 19149 1.9666  = 1967 364 E =t  Interpretation of the findings x−E x+E 62306 − 1967    62306 + 1967 $60,339    $64273 We are 95% confident that the interval from $60,339 to $64,273 actually does contain the true value of the population proportion p Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown  s 2 n 19149 2.588  = 2597 364 Now we find the confidence level E =t  x−E x+E 62306 − 2597    62306 + 2697 $59,709    $64,903 From this data: We are 99% confident that the interval from $59,709 to $64,903 actually does contain the true value of the population proportion p. Comparing intervals and conclusions There was noticeable change. A 95% Confidence Interval is narrower than a 99% Confidence Interval. This occurs because the as the precision of the confidence interval increases (ie CI width decreasing), the reliability of an interval containing the actual mean decreases (less of a range to possibly cover the mean). When defining confidence intervals, the higher your confidence level is, the wider your confidence interval range will become. This proves true as with the 95% confidence level, our confidence interval range is $60,339 to $64,273, this range increases in width when using a 99% confidence level, resulting in a confidence interval range of $59,709 to $64,903. References Lapp, J., & Triola, M. F. (2014). Students solutions manual, Essentials of statistics, fifth edition, Mario F. Triola. Boston: Pearson. Running head: HYPOTHESIS TESTING 1 Hypothesis testing HYPOTHESIS TESTING 2 Hypothesis testing A statistical hypothesis normally describes an assumption made regarding a parameter of a population. The hypothesis may be true or false. Hypothesis testing, therefore, defines procedures that are followed before accepting or rejecting a statistical hypothesis. These procedures include; 1. Formulating the test hypothesis This step involves formulating the null hypothesis and the alternative hypothesis. Denoted by H0 the null hypothesis describes the assumption that the negation of the research question while the alternative hypothesis H1 represents the research hypothesis or what statistician is attempting to prove. 2. Deciding the direction of the test The test could be a left-tailed test, right-tailed test, or two-tailed depending on the research hypothesis. The right-tailed test occurs when the research attempts to determine if the sample parameter is greater compared to the hypothesized value whilst the left-tailed test is deployed when the researcher tries to determine if the sample parameter is less compared to the hypothesized value (DeGroot & Schervish, 2012). A two-tailed test tries to determine if there is any statistically significant difference between the sample parameter and the hypothesized value. 3. Deciding the test statistic The z-test s used when the population variance is known and that sample size is significantly large i.e. n is greater than 30. The t-test, on the other hand, is used when the population variance and standard deviation are unknown and the sample size is small. HYPOTHESIS TESTING 3 4. Evaluating the test-statistic The test-statistic defines a numerical summary of a sample data which reduces the whole sample into a single value that can be utilized in the hypothesis test. In the case of the t-test, the test statistic is evaluated by the following formula; 𝑡 − 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 = 𝑥̌ − 𝜇 𝑠 √𝑛 Where the 𝑥̌ represents the sample mean, µ represents the hypothesized value, s represents the sample standard deviation, and n represents the sample size. In the case of z-test, the t-test is evaluated as below; 𝑧 − 𝑡𝑒𝑠𝑡 = 𝑥̌ − 𝜇 𝜎 √𝑛 Where σ represents the population standard deviation 5. P-value The P-value aids in determining the significance of the test-test results. A p-value less than the alpha level of significance indicates that there is a sufficient ground for rejecting the H0 while a p-value greater than the level of significance indicates that the test-results are insignificance, and as such the H0 is not discarded. The p-value for the test-statistic can be obtained by using the z tables in the case of z-test or the t-table in the case of the t-test. 6. Determining the critical value HYPOTHESIS TESTING The next step is to determine the critical value corresponding to the alpha level of significance. A critical point defines a point of the distribution used in the test which is paired with the test statistic to decide whether to discard or accept the null hypothesis. 7. Making the decision The decision whether to discard or accept the H0 is based upon the p-value or the critical value. When the p-value is less than alpha, the H0 is rejected otherwise it’s accepted. However, using the critical value approach, the null hypothesis is discarded when the test-statistics is greater than the critical value and accepted, otherwise (Chatfield et al., 2010). 8. Making a conclusion The last step in to make a conclusion about the research hypothesis or question in relation to the dataset. When making a decision, the P-value and the critical value approach give similar results as such, either method can be appropriate for the hypothesis test. Performing hypothesis test 1. Formulating hypothesis H0: µ=65,000 H1: µ
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Running head: COURSE PROJECT: PHASE 4

COURSE PROJECT: PHASE 4
Name:
Institution affiliation:
Date:

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COURSE PROJECT: PHASE 4

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COURSE PROJECT: PHASE 4

Introduction of case scenario and data set
The dataset comprise of the information about the 364 job titles in the state of Minnesota.
The salary allocated for these job title is within a range of $40,000 - $120,000. This case scenario
has got two variables; the job title which is a qualitative variable and salary which is a quantitative
variable. The job title is a qualitative variable since its data has no numeric property whereas the
salary is a quantitative variable because its data has a numeric property. The salary variable is
continuous due to the fact that someone’s salary is bound to change annually due to many factors
such as promotions, experience in the job, pay increment, etc.
Through the identification of the quantitative and qualitative variables, it is possible to
accurately identify the measurement level for both variables. In this regards, the job title can be
categorized as a nominal measurement since it doesn't have a numerical significance. On the other
hand, the salary can be considered a ratio measurement since there is no absolute zero in payment.

The importance of the Measures of Center and the Measures of Variation
The Measures of Center provide representative values which summarize the data sets. They
include the mean, mode, median, and midrange. Generally, the mean is the most vital numerical
measurement when it comes to data description. It indicates the average of all the values implying
that each value is used in the computation of the mean. However, an extreme outlier can change
the value of the mean significantly. Thus, the mean is not a resistant measure of center. The median
I generally regarded as the middle value since half of the values in the data set is greater than the
median and half are less than the median. An important property of the median is that it is a
resistant measure of center since the mean doesn’t change by a significant amount as a result of

COURSE PROJECT: PHASE 4

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the inclusion of a few extreme values. The mode is the value that occurs frequently in a data set.
The mode can be found in both...


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