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. Describe the 8 steps in the process for hypothesis testing. Include an explanation of the decision criteria for rejec

hypothesis for both the p-value method and the critical value method.

e decision criteria for rejecting the null

2. A claim is made that the average salary for all jobs in Minnesota is less than $74,000. You are going to test the

claim using ðœ¶ = ðŸŽ. ðŸŽðŸ“ and assume that your data is normally distributed and the population standard deviation

is not known.

2a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify

if the test is left-tailed, right-tailed, or two-tailed and explain why.

2b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test

statistic.

Provide your calculations in the cells designated to the right. Explain your answers below.

2c. What is the critical value? Describe the rejection region of this hypothesis test.

Provide your calculations in the cells designated to the right. Explain your answers below.

2d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain

After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

2e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does

this match your results from the critical value method?

Provide your calculations in the cells designated to the right. Explain your answers below.

u are going to test the

n standard deviation ðˆ

the claim. Then identify

d the value of the test

null hypothesis? Explain.

he original claim.

Calculations/Values

Mean (x-bar)

Standard Deviation

n

mu

Test Statistic

Critical Value

P-value

Formulas/Answers

value. Does

3. A claim is made that the average salary for all jobs in Minnesota is greater than $70,800. You are going to test the

claim using ðœ¶ = ðŸŽ. ðŸŽðŸ“ and assume that your data is normally distributed and the population standard deviation

is not known.

3a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify

if the test is left-tailed, right-tailed, or two-tailed and explain why.

3b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test

statistic.

Provide your calculations in the cells designated to the right. Explain your answers below.

3c. What is the critical value? Describe the rejection region of this hypothesis test.

Provide your calculations in the cells designated to the right. Explain your answers below.

3d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain

After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

3e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does

this match your results from the critical value method?

Provide your calculations in the cells designated to the right. Explain your answers below.

You are going to test the

n standard deviation ðˆ

the claim. Then identify

d the value of the test

null hypothesis? Explain.

he original claim.

Calculations/Values

Mean (x-bar)

Standard Deviation

n

mu

Test Statistic

Critical Value

P-value

Formulas/Answers

value. Does

1.

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

In prior engagements, you have already explained to your client about the basic statistics and

discussed the importance of constructing confidence intervals for the population mean. Your

client says that he remembers a little bit about hypothesis testing, but he is a little fuzzy. He asks

you to give him the full explanation of all steps in hypothesis testing and wants your conclusion

about two claims concerning the average salary for all jobs in the state of Minnesota.

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.

Hypothesis Test Overview

ï‚·

Steps of Hypothesis Test

o Step 1: Identify the claim to be tested and present it in symbolic form.

o

Step 2: Write the null and alternative hypotheses.

o

Step 3: Determine the significance level.

o

Step 4: Identify the test statistic and the direction of the test.

o

Step 5: Determine the decision criteria (Critical value method or P-Value

method)

ï‚§ Critical Value Method: If the test statistic is more extreme than the

critical value(s), reject the null hypothesis.

ï‚§ P-Value Method: If the P-value is less than or equal to ð›¼, reject the

null hypothesis.

o

Step 6: Find the test statistic, then:

ï‚§ Find the P-Value OR

ï‚§ Find the critical value

o

Step 7: Make a decision on the null hypothesis (reject or do not reject)

o

Step 8: State a conclusion about the original claim (the evidence does support

the claim or the evidence does not support the claim)

ï‚·

Null Hypothesis

o ALWAYS uses an equal sign

ï‚·

Alternative Hypothesis

o

Claim uses â€˜equal toâ€™ type language

ï‚§ ð»0 uses an equal sign

ï‚§ ð»ð‘Ž uses a not equal to sign

ï‚§ Two-tailed test

ï‚§ Decision Criteria

ï‚§ If the test statistic is less than the negative critical value or

greater than the positive critical value reject ð»0 and conclude

that the evidence does not support the claim.

ï‚§ If the test statistic is between the two critical values do not

reject ð»0 and conclude that the evidence supports the claim.

ï‚·

o

Claim uses â€˜not equal toâ€™ type language

ï‚§ ð»0 uses an equal sign

ï‚§ ð»ð‘Ž uses a not equal to sign

ï‚§ Two-tailed test

ï‚§ Decision Criteria

ï‚§ If the test statistic is less than the negative critical value or

greater than the positive critical value reject ð»0 and conclude

that the evidence supports the claim.

ï‚§ If the test statistic is between the two critical values do not

reject ð»0 and conclude that the evidence does not support the

claim.

o

Claim uses â€˜less thanâ€™ type language

ï‚§ ð»0 uses an equal sign

ï‚§ ð»ð‘Ž uses a less than sign

ï‚§ Left-tailed test

ï‚§ Decision Criteria

ï‚§ If the test statistic is less than the critical value reject ð»0 and

conclude that the evidence supports the claim.

ï‚§ If the test statistic is greater than the critical value do not reject

ð»0 and conclude that the evidence does not support the claim

o

Claim uses â€˜greater thanâ€™

ï‚§ ð»0 uses an equal sign

ï‚§ ð»ð‘Ž uses a greater than sign

ï‚§ Right-tailed test

ï‚§ Decision Criteria

ï‚§ If the test statistic is greater than the critical value then reject

ð»0 and conclude that the evidence supports the claim

ï‚§ If the test statistic is less than the critical value do not reject ð»0

and conclude that the evidence does not support the claim

Critical Value Excel Formulas

o

Left-tailed:

ï‚§ ð‘¡ statistic: =T.INV(alpha, d.o.f.)

ï‚§

ð‘§ statistic: =NORM.S.INV(alpha)

ï‚§

ðœ’ 2 statistic: =CHISQ.INV(alpha, d.o.f.)

o

o

ï‚·

Right-tailed:

ï‚§ ð‘¡ statistic: =T.INV(1-alpha, d.o.f.)

ï‚§

ð‘§ statistic: =NORM.S.INV(1-alpha)

ï‚§

ðœ’ 2 statistic: =CHISQ.INV.RT(alpha, d.o.f.)

Two-tailed:

ï‚§ ð‘¡ statistic: =T.INV(1-alpha/2, d.o.f.) and then uses both positive and

negative values

ï‚§

ð‘§ statistic: =NORM.S.INV(1-alpha/2) and then uses both positive and

negative values

ï‚§

ðœ’ 2 statistic: both =CHISQ.INV(alpha/2, d.o.f.) and

=CHISQ.INV.RT(alpha/2, d.o.f.)

P-Value Excel Formulas

o

o

o

Left-tailed:

ï‚§

ð‘¡ statistic: =T.DIST(test stat, d.o.f., TRUE)

ï‚§

ð‘§ statistic: =NORM.S.DIST(test stat, TRUE)

ï‚§

ðœ’ 2 statistic: =CHISQ.DIST(test stat, d.o.f., TRUE)

Right-tailed:

ï‚§ ð‘¡ statistic: =1-T.DIST(test stat, d.o.f., TRUE)

ï‚§

ð‘§ statistic: =1-NORM.S.DIST(test stat, TRUE)

ï‚§

ðœ’ 2 statistic: =CHISQ.DIST.RT(test stat, d.o.f., TRUE)

Two-tailed: use left-tailed formulas shown above for a negative test statistic or

right-tailed formula for a positive test statistic

ï‚·

Test Statistic and Critical Value Types

o

ï‚·

The test statistic will always be the same type of statistic as the critical value.

Which one you use depends on the parameter being tested.

ï‚§

Claims about a mean will use a ð‘¡ statistic and the T. formulas for

critical values and P-Values.

ï‚§

Claims about a proportion will use a ð‘§ statistic and the NORM.S

formulas for critical values and P-Values.

ï‚§

Claims about a standard deviation will use a ðœ’ 2 statistic and the

CHISQ. Formulas for critical values and P-Values.

Test Statistic Formulas

ï‚·

Tests about a Population Proportion

o

Use a ð‘§ test statistic and a ð‘§ critical value(s)

o

ð‘§ âˆ’ ð‘¡ð‘’ð‘ ð‘¡ =

ð‘Ì‚âˆ’ð‘

ð‘ð‘ž

ð‘›

âˆš

ï‚§

ï‚·

Tests about a Population Mean

o

Use a ð‘¡ test statistic and a ð‘¡ critical value(s)

o

ð‘¡ âˆ’ ð‘¡ð‘’ð‘ ð‘¡ =

ï‚§

ï‚·

ð‘ is determined by ð»0

ð‘¥Ì… âˆ’ðœ‡

ð‘

âˆšð‘›

ðœ‡ is determined by ð»0

Tests about a Population Standard Deviation

o

Use a ðœ’ 2 (chi-squared) test statistic and a ðœ’ 2 critical value(s)

o

ðœ’2 =

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(ð‘›âˆ’1)ð‘ 2

ðœŽ2

ðœŽ is determined by ð»0

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Comparing Two Population Proportions

o

Use a ð‘§ test statistic and a ð‘§ critical value(s)

o

Test statistic:

ð‘§=

(ð‘Ì‚1 âˆ’ ð‘Ì‚ 2 ) âˆ’ (ð‘1 âˆ’ ð‘2 )

ð‘Ì… ð‘žÌ… ð‘Ì… ð‘žÌ…

ð‘›1 + ð‘›2

âˆš

ð‘¥

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ð‘Ì‚1 = ð‘›1 , sample proportion from 1st sample

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ð‘Ì‚2 = ð‘›2 , sample proportion from 2nd sample

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ð‘1 â€“ population proportion from 1st population

ð‘2 â€“ population proportion from 2nd population

From ð»0 , assume ð‘1 = ð‘2, i.e. ð‘1 âˆ’ ð‘2 = 0

ð‘¥ +ð‘¥

ð‘Ì… = ð‘›1 +ð‘›2 , pooled proportion

ð‘¥

1

2

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1

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2

ð‘žÌ… = 1 âˆ’ ð‘Ì…

ð‘›1 â€“ sample size from 1st population

ð‘›2 â€“ sample size from 2nd population

Comparing Two Means, Independent Samples

o

Use a ð‘¡ test statistic and a ð‘¡ critical value(s)

o

Test statistic:

ð‘¡=

(ð‘¥Ì…1 âˆ’ ð‘¥Ì…2 ) âˆ’ (ðœ‡1 âˆ’ ðœ‡2 )

ð‘ 2 ð‘ 2

âˆš 1+ 2

ð‘›1 ð‘›2

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ð‘¥Ì…1 â€“ sample mean from 1st sample

ð‘¥Ì…2 â€“ sample mean from 2nd sample

ðœ‡1 â€“ population mean from 1st population

ðœ‡2 â€“ population mean from 2nd sample

From ð»0 , assume ðœ‡1 = ðœ‡2 , i.e. ðœ‡1 âˆ’ ðœ‡2 = 0

ð‘ 1 â€“ sample standard deviation from 1st sample

ð‘ 2 â€“ sample standard deviation from 2nd sample

ð‘›1 â€“ sample size from 1st population

ð‘›2 â€“ sample size from 2nd population

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Comparing Dependent Samples, Matched Pairs

o

o

Use a ð‘¡ test statistic and a ð‘¡ critical value(s)

Test statistic:

ð‘‘Ì… âˆ’ ðœ‡ð‘‘

ð‘¡ âˆ’ ð‘¡ð‘’ð‘ ð‘¡ = ð‘

ð‘‘

âˆšð‘›

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ð‘‘ â€“ difference between two matched pairs

ð‘‘Ì… â€“ average difference between matched pairs in sample

ðœ‡ð‘‘ â€“ average difference between matched pairs in population,

determined by ð»0

ð‘ ð‘‘ â€“ standard deviation of the differences of matched pairs

ð‘› â€“ number of pairs

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