Module 05 focuses on hypothesis testing using two samples, covering independent and dependent samples, and their respective testing procedures. It emphasizes the importance of determining the relationship between sample data and provides examples for various contexts, including weights of cola cans, creativity scores based on background color, and seat belt effectiveness on ICU stays. Key concepts include null and alternative hypotheses, test statistics, and significance levels, with a brief overview of how inferential statistics aids in forming conclusions about population parameters.

1. Module 05 –
Hypothesis Tests Using Two Samples
Class Objectives:
· Identify whether two samples are independent or dependent.
· Compare the testing procedures for two sample tests.
· Test hypothesis about two population parameters.
Module 05 - Part 1
Last week we took one sample to see if it supported our
alternative hypothesis. This week we are going to increase to
TWO samples and see if there is a significant difference
between them.
When would we use this?
· Two samples are __________________ ________________ if
the sample values from one population are not related to or
somehow naturally paired or matched with the sample values
from the other population.
· Example:
· Two samples are _____________________________ (or
consist of ______________________________________) if the
sample values are somehow matched, where the matching is
based on some inherent relationship.
· Example:

2. Hint: If the two samples have different sample sizes with no
missing data, they must be independent. If the two samples have
the same sample size, the samples may or may not be
independent.
Put the variables in for each population in the table below.
Population 1
Population 2
Population Mean
Population Standard Deviation
Population Proportion
Sample Size
Sample Mean
Sample Standard Deviation
Sample Proportion
Note: We are going to approach the problem as if are unknown.
This is the most common and means that we will be using the t
test statistic.

3. · The test statistic is given by the formula below:
where we assume .
To calculate the degrees of freedom, pick the
_______________________ n value and subtract 1.
We will be doing the same steps as before to test the hypothesis
(either critical value or p-value test). There are just different
formulas.
· The null hypothesis is given as
_____________________________.
· The alternative hypothesis will be either
____________________________,
___________________________, or
_____________________________.
Example 1. Data Set 26 “Cola Weights and Volumes” in
Appendix B includes weights (lb) of the contents of cans of Diet
Coke (n = 36, x = 0.78479 lb, s = 0.00439 lb) and of the
contents of cans of regular Coke (n = 36, x = 0.81682 lb, s =
0.00751 lb). Use a 0.05 significance level to test the claim that
the contents of cans of Diet Coke have weights with a mean that
is less than the mean for regular Coke.

4. Example 2. Researchers from the University of British
Columbia conducted trials to investigate the effects of color on
creativity. Subjects with a red background were asked to think
of creative uses for a brick; other subjects with a blue
background were given the same task. Responses were scored
by a panel of judges and results from scores of creativity are
given below. Higher scores correspond to more creativity. The
researchers make the claim that “blue enhances performance on
a creative task.” Use a 0.05 significance level to test the claim
that blue enhances performance on a creative task.
Example 3.A study of seat belt use involved children who were
hospitalized after motor vehicle crashes. For a group of 123
children who were wearing seat belts, the number of days in
intensive care units (ICU) has a mean of 0.83 and a standard
deviation of 1.77. For a group of 290 children who were not
wearing seat belts, the number of days spent in ICUs has a mean
of 1.39 and a standard deviation of 3.06. Use a 0.01 significance
level to test the claim that children wearing seat belts have a
lower mean length of time in an ICU than the mean for children

5. not wearing seat belts.
Module 05 - Part 2
Inferential statistics involves forming conclusions about
population parameters.
· These population parameters could be:
The activities that we could perform on two samples are
estimating the value of the population parameters using
confidence intervals and testing claims made about the
population parameters.
Independent Samples
Dependent Samples
Samples taken from two different populations, where the
selection process for one sample is independent of the selection
process for the other sample.
Samples taken from two populations where either (1) the
element samples is a member of both populations or (2) the
element samples in the second population is selected because it
is similar on all other characteristics, or “matched,” to the
element selected from the first population.
Example.

6. Example.
The hypothesis Test for two dependent samples is a bit different
because we need to use the difference from each matched pair to
test the claim.
The null and alternative hypotheses are different for dependent
samples as well.
· Null Hypothesis
___________________
· Alternative Hypothesis
____________________
The difference between the means is less than 0 (negative).
Thus, the first group has smaller mean values.
____________________
The difference between the means is greater than 0 (positive).
Thus, the first group has larger mean values.
· The test statistic for dependent samples uses the following

7. formula:
Example 4. Here we consider one aspect of how we treat women
and men differently based on their ages. Data Set 14 “Oscar
Winner Age” in Appendix B lists ages of actresses when they
won Oscars in the category of Best Actress, along with the ages
of actors when they won Oscars in the category of Best Actor.
The ages are matched according to the year that the awards were
presented. Table 9-2 includes a small random selection of the
available data so that we can better illustrate the procedures of
this section. Use the sample data in Table 9-2 with a 0.05
significance level to test the claim that for the population of
ages of Best Actresses and Best Actors, the differences have a
mean less than 0 (indicating that Best Actresses are generally
younger than Best Actors).
Example 5. A popular theory is that presidential candidates
have an advantage if they are taller than their main opponent.
Listed are heights (cm) of presidents along with the heights of
their main opponents. Use the sample data with a 0.05
significance level to test the claim that for the population of

8. heights of presidents and their main opponents, the differences
have a mean greater than 0 cm.
Module 05 SummaryVariables
· Independent Samples
· Dependent Samples
· – difference between the two values in a matched pair
· – population mean of all the differences of the population
· – sample mean of all the differences in the sample data
· – sample standard deviation of all the differences in the
sample data
· – number of pairs of dataExcel Formulas
· Independent Samples
· To calculate the test statistic:
· To calculate the degrees of freedom, pick the smaller n value
and subtract 1.
· Dependent Samples
· To calculate the test statistic in Excel: “= /(/SQRT(n))”
· To calculate the degrees of freedom:
2
Allisha Langdon Rasmussen College B094 Geometry
STA3215CBE - Statistics Allisha Wise Page 7
Example 1 (Indep)Diet CokeRegular Coken136n236x-bar
10.78479x-bar 20.81682s10.00439s20.00751test statCVp-value
Example 2 (Indep)Red BackgroundBlue Backgroundn135n236x-
bar 13.39x-bar 23.97s10.97s20.63test statCVp-value
Example 3 (Indep)Wearing SeatbeltsNOT Wearing
Seatbeltsn1123n2290x-bar 10.83x-bar 21.39s11.77s23.06test
statCVp-value
Example 4 (dep)Actress (years)Actor (years)Difference

9. d28622837Mean of Differences (d-bar)3136Standard Deviation
of Differences (s_d)29383529Test StatisticCritical Valuep-value
Example 5 (dep)Height of President (cm)Height of Main
Opponent (cm)Difference d185171178180Mean of Differences
(d-bar)175173Standard Deviation of Differences
(s_d)183175193188Test Statistic173178Critical Valuep-value
DataJob TitleSalaryAccountants and Auditors67280source:
http://www.bls.gov/Actuaries100580Administrative Law Judges,
Adjudicators, and Hearing
Officers144840Calculations/ValuesFormulas/AnswersAdministr
ative Services Managers97180MeanAdult Basic and Secondary
Education and Literacy Teachers and Instructors63940Standard
DeviationAdvertising and Promotions
Managers105130nAdvertising Sales Agents51740Aerospace
Engineering and Operations Technicians57140Aerospace
Engineers115220Agents and Business Managers of Artists,
Performers, and Athletes74580Agricultural and Food Science
Technicians40060Agricultural Inspectors54140Agricultural
Sciences Teachers, Postsecondary87390Air Traffic
Controllers114906Aircraft Cargo Handling
Supervisors50380Aircraft Structure, Surfaces, Rigging, and
Systems Assemblers51410Airfield Operations
Specialists59800Airline Pilots, Copilots, and Flight
Engineers115670Anthropologists and
Archeologists51720Appraisers and Assessors of Real
Estate52870Arbitrators, Mediators, and
Conciliators86430Architects, Except Landscape and
Naval81000Architectural and Civil Drafters62210Architecture
and Engineering Occupations73850Architecture Teachers,
Postsecondary73870Archivists76749Art Directors98924Art,
Drama, and Music Teachers, Postsecondary78700Athletic
Trainers45440Atmospheric and Space
Scientists93900Atmospheric, Earth, Marine, and Space Sciences
Teachers, Postsecondary96590Audiologists97230Avionics
Technicians47320Biomedical

10. Engineers101250Boilermakers76310Broadcast News
Analysts71040Brokerage Clerks57260Budget
Analysts75940Business and Financial Operations
Occupations64880Business Operations Specialists, All
Other67980Business Teachers, Postsecondary109800Buyers and
Purchasing Agents, Farm Products62290Camera and
Photographic Equipment Repairers32280Captains, Mates, and
Pilots of Water Vessels63890Cardiovascular Technologists and
Technicians59630Career/Technical Education Teachers, Middle
School69050Career/Technical Education Teachers, Secondary
School63430Cargo and Freight Agents40910Cartographers and
Photogrammetrists72120Chefs and Head Cooks47660Chemical
Engineers87200Chemical Equipment Operators and
Tenders45460Chemical Plant and System
Operators54920Chemical Technicians50360Chemistry Teachers,
Postsecondary96330Chemists59630Child, Family, and School
Social Workers58140Chiropractors87540Civil
Engineers91430Claims Adjusters, Examiners, and
Investigators66030Clinical, Counseling, and School
Psychologists76150Coil Winders, Tapers, and
Finishers36610Commercial and Industrial
Designers66710Commercial Pilots130059Communications
Equipment Operators, All Other43160Communications
Teachers, Postsecondary85310Community and Social Service
Occupations43790Community Health
Workers37190Compensation and Benefits
Managers123570Compensation, Benefits, and Job Analysis
Specialists67210Compliance Officers67637Computer and
Information Research Scientists121310Computer and
Information Systems Managers137140Computer and
Mathematical Occupations81640Computer Hardware
Engineers95500Computer Network Architects115050Computer
Network Support Specialists70940Computer Occupations, All
Other92960Computer Programmers84280Computer Science
Teachers, Postsecondary89290Computer Systems
Analysts90600Computer User Support

11. Specialists53680Conservation Scientists67540Construction and
Building Inspectors64150Construction
Managers99150Continuous Mining Machine
Operators55330Control and Valve Installers and Repairers,
Except Mechanical Door64960Conveyor Operators and
Tenders35110Cost Estimators69480Crane and Tower
Operators53980Credit Analysts72870Credit
Counselors46720Criminal Justice and Law Enforcement
Teachers, Postsecondary66980Curators66230Database
Administrators91730Dental Hygienists71930Derrick Operators,
Oil and Gas38120Detectives and Criminal
Investigators90890Diagnostic Medical
Sonographers74340Dietitians and Nutritionists60370Directors,
Religious Activities and Education43690Drafters, All
Other51790Economics Teachers,
Postsecondary137920Economists106280Editors58820Educa tion
Administrators, All Other79960Education Administrators,
Elementary and Secondary School103570Education
Administrators, Postsecondary110110Education Administrators,
Preschool and Childcare Center/Program81590Education
Teachers, Postsecondary65020Education, Training, and Library
Occupations47920Educational, Guidance, School, and
Vocational Counselors56550Electric Motor, Power Tool, and
Related Repairers63800Electrical and Electronics
Drafters69010Electrical and Electronics Engineering
Technicians68060Electrical and Electronics Installers and
Repairers, Transportation Equipment54060Electrical and
Electronics Repairers, Commercial and Industrial
Equipment55970Electrical and Electronics Repairers,
Powerhouse, Substation, and Relay81590Electrical
Engineers91870Electrical Power-Line Installers and
Repairers67430Electricians60590Electro-Mechanical
Technicians54700Electronics Engineers, Except
Computer100610Elementary School Teachers, Except Special
Education62620Elevator Installers and
Repairers88340Embalmers48770Emergency Management

12. Directors79270Engineering Technicians, Except Drafters, All
Other63250English Language and Literature Teachers,
Postsecondary81700Environmental Engineering
Technicians56810Environmental Engineers84870Environmental
Science and Protection Technicians, Including
Health45090Environmental Science Teachers,
Postsecondary92530Environmental Scientists and Specialists,
Including Health84320Epidemiologists85620Executive
Secretaries and Executive Administrative
Assistants55770Exercise Physiologists54300Explosives
Workers, Ordnance Handling Experts, and
Blasters62910Extruding, Forming, Pressing, and Compacting
Machine Setters, Operators, and Tenders38680Farm and Home
Management Advisors38940Film and Video
Editors62280Financial Analysts85660Financial Clerks, All
Other44080Financial Examiners101500Financial
Managers142370Financial Specialists, All Other87690Fire
Inspectors and Investigators58590Firefighters49620First-Line
Supervisors of Construction Trades and Extraction
Workers82160First-Line Supervisors of Correctional
Officers84290First-Line Supervisors of Farming, Fishing, and
Forestry Workers43150First-Line Supervisors of Fire Fighting
and Prevention Workers91930First-Line Supervisors of Helpers,
Laborers, and Material Movers, Hand49590First-Line
Supervisors of Landscaping, Lawn Service, and Groundskeeping
Workers54280First-Line Supervisors of Mechanics, Installers,
and Repairers66430First-Line Supervisors of Non-Retail Sales
Workers72920First-Line Supervisors of Office and
Administrative Support Workers58120First-Line Supervisors of
Police and Detectives101240First-Line Supervisors of
Production and Operating Workers60990First-Line Supervisors
of Protective Service Workers, All Other46280First-Line
Supervisors of Transportation and Material-Moving Machine
and Vehicle Operators58250Fish and Game Wardens75430Food
Service Managers51340Foreign Language and Literature
Teachers, Postsecondary73350Forensic Science

13. Technicians79630Forest and Conservation
Technicians46640Foresters65970Forestry and Conservation
Science Teachers, Postsecondary90080Fundraisers57720Funeral
Service Managers82590Gaming Supervisors32220Gas
Compressor and Gas Pumping Station Operators62720Gas Plant
Operators70130General and Operations
Managers124190Geography Teachers,
Postsecondary82530Geological and Petroleum
Technicians39180Geoscientists, Except Hydrologists and
Geographers70730Health and Safety Engineers, Except Mining
Safety Engineers and Inspectors84880Health Diagnosing and
Treating Practitioners, All Other67650Health
Educators41781Health Specialties Teachers,
Postsecondary136670Health Technologists and Technicians, All
Other45940Healthcare Practitioners and Technical
Occupations67470Healthcare Social Workers53600Hearing Aid
Specialists46970Historians84337History Teachers,
Postsecondary88590Hoist and Winch Operators80,660Home
Economics Teachers, Postsecondary74490Human Resources
Managers112430Human Resources Specialists61460Industrial
Engineering Technicians55460Industrial
Engineers82720Industrial Machinery Mechanics55930Industrial
Production Managers100480Information and Record Clerks, All
Other45700Information Security Analysts97360Installation,
Maintenance, and Repair Occupations45990Instructional
Coordinators66810Insurance Appraisers, Auto
Damage70380Insurance Sales Agents66080 Insurance
Underwriters76990Interior Designers62010Judges, Magistrate
Judges, and Magistrates58140Kindergarten Teachers, Except
Special Education55850Labor Relations
Specialists51870Landscape
Architects68960Lawyers140920Layout Workers, Metal and
Plastic42830Legal Occupations82900Legal Support Workers,
All Other60100Librarians56320Library Science Teachers,
Postsecondary78830Life Scientists, All Other82630Life,
Physical, and Social Science Occupations62840Loading

14. Machine Operators, Underground Mining41270Loan
Officers63040Locomotive Engineers71960Logging Workers, All
Other41940Logisticians74600Magnetic Resonance Imaging
Technologists70580Management Analysts92200Managers, All
Other88600Marine Engineers and Naval Architects82410Market
Research Analysts and Marketing Specialists62380Marketing
Managers122260Marriage and Family Therapists55600Materials
Engineers91510Mathematical Science Teachers,
Postsecondary78880Mechanical Drafters58540Mechanical
Engineering Technicians60220Mechanical
Engineers92040Media and Communication Equipment Workers,
All Other76540Medical and Clinical Laboratory
Technologists65770Medical and Health Services
Managers113030Medical Equipment Repairers58310Meeting,
Convention, and Event Planners52370Mental Health
Counselors46580Metal-Refining Furnace Operators and
Tenders44990Middle School Teachers, Except Special and
Career/Technical Education66630Millwrights57190Mine
Cutting and Channeling Machine Operators46250Mine Shuttle
Car Operators56930Mining and Geological Engineers, Including
Mining Safety Engineers93920Mining Machine Operators, All
Other69160Mixing and Blending Machine Setters, Operators,
and Tenders41970Mobile Heavy Equipment Mechanics, Except
Engines58950Model Makers, Metal and Plastic57100Morticians,
Undertakers, and Funeral Directors69800Multimedia Artists and
Animators59890Music Directors and Composers46260Natural
Sciences Managers113620Network and Computer Systems
Administrators87700Nuclear Engineers121650Nuclear Medicine
Technologists79440Nuclear Technicians88770Nurse
Practitioners101960Nursing Instructors and Teachers,
Postsecondary72450Occupational Health and Safety
Specialists75610Occupational Health and Safety
Technicians61740Occupational Therapists82290Occupational
Therapy Assistants61860Operations Research
Analysts90310Optometrists111790Orthotists and
Prosthetists82380Painters, Transportation

15. Equipment45230Paper Goods Machine Setters, Operators, and
Tenders37110Paralegals and Legal
Assistants56990Patternmakers, Metal and Plastic56260Personal
Financial Advisors121750Petroleum Pump System Operators,
Refinery Operators, and
Gaugers66550Pharmacists120280Philosophy and Religion
Teachers, Postsecondary78010Physical Therapist
Assistants58720Physical Therapists90040Physician
Assistants104730Physicists118520Physics Teachers,
Postsecondary89040Plant and System Operators, All
Other56830Plumbers, Pipefitters, and
Steamfitters77570Podiatrists195730Police and Sheriff's Patrol
Officers74870Political Science Teachers,
Postsecondary90250Postal Service Clerks49310Postal Service
Mail Carriers50160Postal Service Mail Sorters, Processors, and
Processing Machine Operators49820Postmasters and Mail
Superintendents75620Power Distributors and
Dispatchers84830Power Plant Operators79100Precision
Instrument and Equipment Repairers, All Other64170Private
Detectives and Investigators58290Probation Officers and
Correctional Treatment Specialists64300Producers and
Directors75970Production, Planning, and Expediting
Clerks48390Property, Real Estate, and Community Association
Managers66710Psychologists, All Other79010Psychology
Teachers, Postsecondary89680Public Relations and Fundraising
Managers115180Public Relations Specialists63620Pump
Operators, Except Wellhead Pumpers51520Purchasing Agents,
Except Wholesale, Retail, and Farm Products61760Purchasing
Managers111380Radiation Therapists84640Radio, Cellular, and
Tower Equipment Installers and Repairers49240Radiologic
Technologists63420Rail Yard Engineers, Dinkey Operators, and
Hostlers54790Railroad Conductors and Yardmasters65740Rail -
Track Laying and Maintenance Equipment Operators54600Real
Estate Brokers88750Real Estate Sales Agents59010Recreation
and Fitness Studies Teachers, Postsecondary60080Recreational
Vehicle Service Technicians34450Refractory Materials

16. Repairers, Except Brickmasons49210Registered
Nurses71730Reinforcing Iron and Rebar
Workers86290Respiratory Therapists56910Rolling Machine
Setters, Operators, and Tenders, Metal and Plastic38060Roof
Bolters, Mining58900Rotary Drill Operators, Oil and
Gas49720Sales Engineers98760Sales Managers75432Sales
Representatives, Services, All Other61930Sales
Representatives, Wholesale and Manufacturing, Except
Technical and Scientific Products69900Sales Representatives,
Wholesale and Manufacturing, Technical and Scientific
Products81950Secondary School Teachers, Except Special and
Career/Technical Education68380Securities, Commodities, and
Financial Services Sales Agents86070Service Unit Operators,
Oil, Gas, and Mining42200Set and Exhibit Designers54620Ship
Engineers57066Signal and Track Switch Repairers38120Social
and Community Service Managers63870Social Scientists and
Related Workers, All Other79960Social Work Teachers,
Postsecondary54580Social Workers, All Other65890Sociology
Teachers, Postsecondary87710Software Developers,
Applications96110Software Developers, Systems
Software106700Soil and Plant Scientists57080Sound
Engineering Technicians58660Special Education Teachers, All
Other59400Special Education Teachers, Kindergarten and
Elementary School65430Special Education Teachers, Middle
School62160Special Education Teachers, Secondary
School68560Speech-Language Pathologists78760Stationary
Engineers and Boiler
Operators79090Statisticians88190Surveyors60215Tank Car,
Truck, and Ship Loaders45470Tax Examiners and Collectors,
and Revenue Agents79850Technical
Writers67410Telecommunications Equipment Installers and
Repairers, Except Line Installers57580Tire Builders42500Tool
and Die Makers54680Training and Development
Managers101500Training and Development
Specialists59910Transportation Inspectors86790Transportation,
Storage, and Distribution Managers93250Urban and Regional

17. Planners79510Veterinarians93830Water and Wastewater
Treatment Plant and System Operators54560Web
Developers57450Wholesale and Retail Buyers, Except Farm
Products55080Writers and Authors53050Zoologists and
Wildlife Biologists62420
Question 1
1. Describe the 8 steps in the process for hypothesis testing.
Include an explanation of the decision criteria for rejecting the
null hypothesis for both the p-value method and the critical
value method.
Question 2Calculations/ ValuesFormulas/AnswersMean (x-
bar)Standard DeviationnmuTest StatisticCritical ValueP-value
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

18. 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.
Question 3Calculations/ValuesFormulas/AnswersMean (x-
bar)Standard DeviationnmuTest StatisticCritical ValueP-value
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

19. 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.