Shoe size and height correlation chart

IB Math Studies 2011 12 Project Tables of Contents

A. Description, criteria, grading and due dates B. Requirements C. Guidelines D. Existing Data Sources and Projects E. Generating your own data and Project Ideas F. Simple Math Processes G. Sophisticated Math Processes H. Rough draft assignments and due dates I. Example Project Titles and Statements of Task J. IBO Criteria / Grading Rubric

There is no one best method of research for all situations. Rather, there are a wide variety of techniques for the researcher to choose from. There are three basic methods of research: 1) survey, 2) observation, and 3) experiment. Each method has its advantages and disadvantages.

The survey is the most common method of gathering information in the social sciences. Surveys can be face to face; by telephone, or questionnaire, or by mail.

Observation research does not directly interacting with people or situation being studied. It has been used for many years by A.C. Nielsen to monitor television viewing habits. The fastest growing form of observation research has been made possible by internet “cookies” which track our internet usage and direct us to advertisers who are trying to find us. Also, bar code scanners at cash registers also collect information about us as consumers.

In an experiment, one or more variables over are changed during the research. When all other variables are held constant (except the one being manipulated), changes in the dependent variable can be explained by the change in the independent variable.

Obtaining data for statistical research all comes from one of the above described methods: surveys, observation, or experiments. For your Math Studies project, you should begin deciding which method you are most interested in using.

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A. Description, criteria, grading and due dates

A project is about applying what you know in a task you define. This IB Project is an application of the mathematics studied in the course. The project involves the collection and/or generation of data, and the analysis and evaluation of that data. This involves the collection of information or the generation of measurements, and the analysis and evaluation of the information or measurements. Technology is required mainly the TI 83 or 84 graphing calculator. But other math software programs like Excel, Math Type, Geiger, and Sketchpad among others can be used. Students may choose from a wide variety of project types; for example, modeling, investigations, applications and statistical surveys. Projects may take the form of mathematical modeling, investigations, applications, statistical surveys, etc. Failure to do a math studies project will result in a forfeiture of the IB diploma.

Rubric for IB Marking

Criterion A 2 points Introduction

Criterion B 3 points Information / Measurement Criterion C 5 points Mathematical processes Criterion D 3 points Interpretation of results Criterion E 2 points Validity

Criterion F 3 points Structure and communication

Criterion G 2 points Commitment

Deadlines/ Due Dates: There are 8 project deadlines; each is worth one test grade for LHS grade.

Assignment Criterion / Description Due Date LHS Grade Value

Criterion A & B assignment Introduction, Info. & Measurement November 18 one test grade

Criterion C assignment Mathematical processes January 6 one test grade Criterion D assignment Interpretation of results / Validity January 19 one test grade Complete rough draft Submit two copies of rough draft January 24 one test grade Final Project Submit two copies of Final Project February 7 one test grade

IB Internal Assessment Grading

An internal grade of 17 20 is an IB grade of 7 towards the IB diploma. 20 points max 17 20 is a 7 To earn a perfect score of 20, you must earn a “5” in mathematical processes. To do this you must

use at least two sophisticated statistical or math processes including 2 (Chi Squared) and linear

regression. Points will be awarded or deducted from the very beginning on your commitment. A successful project is required for passing this course, and thus for graduation. Plagiarism is a major concern; IB uses turnitin.com among other resources to monitor. Final Project is due February 7th; I need one / two weeks to grade; then one week mailing time to IBO

Moderator.

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B. Requirements

A title (See section below on Example Project Titles and Statements of Task) Statement of the task (See section below on Example Project Titles and Statements of Task) Collected / generated measurements, information / data: ( See section with example projects) An analysis of the measurements, information or data: ( See section with example projects) An evaluation of the analysis: ( See section with example projects) A bibliography and footnotes, as appropriate. ( See section with example projects) First requirement is there must be obtainable data that relates to your research question and project. You must explain in your opening “Statement of task” why your topic is of interest to you. Project must be your own individual research project. Collaboration with peers / teachers is allowed

to both receive and / or provide assistance Must have bibliography; you can use an bibliography application such as “citation machine” or

“easy bib”—both are automatic bibliographies You need to have a minimum of 40 pieces of data for your research project. Must show your work in addition to using technology. At least by one of every calculation must be

done manually on paper. For each math / statistical process an explanation why it was chosen and how that procedure leads to a

pertinent result. The showing of the process is an important grading criterion. When showing work by hand, it is meant showing each step of the calculation along the way, i.e. the

process. This should definitely be done for each mathematical or statistical process used, whether simple or sophisticated at least once.

If your project requires a repeat of a process then you can simply show the calculator output. no minimum or max length—no word count necessary

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C: Guidelines The Math Studies Internal Assessment (Project) is designed for students to use the statistical concepts

taught in the first quarter of the course—so choosing a topic you can find data on is important. Choose a topic of strong interest; and one you can find or generate data on. Make sure there exists sufficient good and reliable data to do your research and investigation project. Data is readily available from numerous reliable government / academic / industry internet sources Or make sure you can generate your own reliable data for your project. Sometimes students have a great idea for a project, but there is not enough reliable data; if you have a

VERY STRONG interest in the topic you still must have at least SOME RELIABLE USEABLE DATA. If your project is lacking in good data, but strong in other aspects, you’ll lose some points (see the

grading rubric and Project Criteria) from IBO. You can choose to use existing data, or create your own data through trials or a survey. Collect additional data in case you need more. I.E. Collect height and weight in addition to Eye Color and

Gender in case you end up needing more data to complete your project. You don’t have to use all of the data you collect, but it can be handy to have it and will be easier to collect in a “one stop shopping or collecting” of your data from the Web, surveys, polls, etc.

Surveys will have to be approved in advance; most students either use existing data from dependable data sources, or create their own data through trials.

About 98% of IB Math Studies Projects end up being statistics and probability based. The best way to ensure your data integrity is to have YOUR OWN TI 83 / 84. There is a class set; but these

cannot leave the school. Data can be entered into EXCEL, which has an excellent chart and graph maker. Data can also be imported from the internet into a software called “Fathom”: Independent Data files can be

imported “clicked and dragged” directly into the FATHOM statistical program Don’t forget to search for pairs of data; such as “medication a blood pressure”. Both Categorical and Quantitative Data can be paired But… Project ideas can come from any area of mathematics, including below:

Not all Math Studies Projects are Statistical. The project can be from other branches of Math including:

NUMBER AND ALGEBRA; SETS AND LOGIC; APPLIED MATH

Sequences and series; Set Notation; Analyzing linear and Quadratic Graphs; Data in Groups of two or three categories; Music, Sports;

GEOMETRY / TRIGONOMETRY AND FUNCTIONS

Calculating angles, distances, areas, volumes (any applied math problem or research question); Estimation of lengths, heights, angles of building or parts of buildings; Analysis of geometrical shapes and designs in building and nature; Applied math with Navigation, Maps, Architecture; Data from science subjects, geography; Trajectories; Waves; Applied math with Natural phenomena such as seasons and tides;

FINANCIAL MATHEMATICS

Financial data from newspapers, banks, etc. on exchange rates, interest rates; information about businesses; computer, car, home sales; Analysis of stock market; U.S. Debt Crisis, Investments, price of precious metals.

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D. Existing Data Sources and Projects General Data Sites:

o http://unstats.un.org/unsd/databases.htm United Nations Statistics Division (UNSD) o http://faostat.fao.org/ Food and Agriculture Organization of the United Nations (FAOSTAT) o http://www.who.int/research/en/ World Health Oranization of the United Nations (disease and healthcare) o http://www.fedstats.gov/ Federal Government Statistics o http://www.eeps.com/zoo/index.html Data Zoo o http://www.dartmouth.edu/~chance/teaching_aids/data.html o DASL The Dataset and Story Library a collection of datasets and related documentation (stories) o http://www.keypress.com/x2814.xml Fathom Data Sites o http://www.keypress.com/x3894.xml Fathom Data Sites o http://www.census.gov/main/www/a2z/ U.S. Census Bureau A to Z: o http://www.census.gov/compendia/statab/ us stat abstract: o http://www.census.gov/population/international/ world population o http://www.census.gov/population/www/popclockus.html U.S. Population:

Economics Research Questions: Statistics and economics can be used to develop solutions to a wide variety of problems faced by governments, corporations, non profit organizations, and other entities.

a) Calculate the percentage change in the Dow Jones Industrial Average from the close on Thursday the 12th to the close on Friday the 13th for every Friday the 13th beginning in 1980. Is the average percentage change substantial?

b) Is wealth in the United States becoming more concentrated or more spread out over the past 30 Years? c) Does legalized gambling raise revenues for a state or county? d) Do 4 day school weeks save money for school districts? e) Economic losses due to park closures: When parks or beaches are closed due to oil or chemical spills, governments

often seek to assess damages associated with visitor losses. How severe were Florida’s economic losses due to lost tourism in 2010 11 due to the BP oil spill—has revenue from tourism decreased in 2010 11 compared to previous years / decades?

f) U.S. companies that move factories to undeveloped nations barely pay employees enough to live on. The United States economy has been suffering its worst unemployment in a generation. Are U.S. companies moving more jobs to foreign countries during the 2000’s than they did during the 1990’s?

g) Recently the Governor of Florida turned away a federal grant of approximately 2 billion dollars to build high speed rail between Tampa, Orlando, and Miami. The reason given was that studies predicted there would not be enough ridership to make rail between the cities profitable. Can you find data to statistically support this?

Economics Data Sources

a) http://www.esa.doc.gov/about economic indicators U.S. Economics and Statistics Association b) http://www.bls.gov/data/ U.S. Department of Labor Bureau of Labor Statistics c) http://research.stlouisfed.org/fred2/ Federal Reserve Economic Data (FRED) d) http://www.econdata.net/ EconData.net e) http://www.fedstats.gov/ Federal Statistics (FEDSTATA) f) http://www.brillig.com/debt_clock/ National Debt Clock and Information g) http://www.worldbank.org/ World Bank: h) http://www.imf.org/external/data.htm International Monetary Fund Data and Statistics

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Environment /Climate / Agriscience /Engineering / Energy

a) Which are more accurate for a particular chosen city: the predicted high or predicted low temperatures? b) The Dead sea has declined 4 feet in depth. If the Dead sea continues losing water at this rate, when would it be

completely gone? c) the rainfall one year correlated positively, negatively, or not at all with the rainfall the previous year? d) The Chashowitzka and Homossasa Rivers have increasing Salinity Rates. Is there a correlation with increased

water consumption in Citrus and Hernando counties? e) Is wind energy really that cheap, effective practical? f) Recent statistics state that one acre of South American rainforest is clear – cut or cleared for development

or cattle rising every second. At this rate, when would South American rain forest disappear? g) Are electric vehicles helping to save the U.S. from importing oil? h) Global warming – summer of 2011 is described as the second hottest summer ever on record. i) One year after the BP Gulf oil spill: are water temperatures higher in the gulf? Are there more scallops and

other fish species that migrated away from the immediate spill area? Are people buying as much Gulf of Mexico seafood now as before the oil spill? (There are lots of potential research questions, and lots of data available on this topic!)

j) Do the numbers of manatee deaths in Kings Bay over the past decade justify the Federal Government mandating minimum / idle boating speeds year round?

k) Are the world’s oceans being, or have they already been overfished? Are certain species of fish (wild salmon, or others) now below a certain number never to return to previously existing levels?

l) In Yellowstone National Park. Several times each day, “old Faithful” has an eruption that lasts 1 to 5 minutes and sends hot water and steam more than 100 feet in the air. The National Park Service posts a sign predicting when the next eruption will occur. Is the interval of time between eruptions well described by the bell shaped normal distribution? Can this interval be predicted with reasonable accuracy from the duration of the preceding eruption?

m) Watch the film Erin Brokovich. The film portrays Bokovich’s life story and how she won the largest the largest settlement ever paid in an environmental damage direct action lawsuit in US history.

n) Antibiotics are commonly given to farm animals and cattle to keep them healthy. Are antibiotics being administered to our food supply causing germ resistance to antibiotics in people?

Environment /Climate / Agriscience / Energy / Engineering Data Sources

o http://www.ncdc.noaa.gov/oa/ncdc.html National Center for Climatic Data (NCDC) o http://www.noaa.gov/index.html National Oceanic Atmospheric Administration (NOAA) o http://www.epa.gov/enviro/html/ef_overview.html U.S. Environmental Protection Agency: (EPA) o http://www.nrel.gov/rredc/ National Renewable Energy Laboratory: (NREL) o http://www.afdc.energy.gov/afdc/ Alternative Fuels and Advanced Vehicles Data Center o http://www.unep.org/ United Nations Environment Program (UNEP) o http://www.ipcc.ch/ Intergovernmental Panel On Climate Change (IPCC) o http://www.nhc.noaa.gov/ National Hurricane Center o http://www.weather.gov/ National Weather Service o http://swera.unep.net/index.php?id=7 Data for Solar and Wind Renewable Energy (SWERA) o http://www.seattlecentral.edu/qelp/index.html Quantitative Environmental Learning Project (QELP)

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Medicine & Public Health

Epidemiology is the study of health patterns in society. It is the cornerstone method of public health research. This research helps governments determine policy to help people become and stay healthier, as well as prevent disease. This is done by identifying risk factors and trying to find associations between factors, or cause. Epidemiologists work on designing studies and collect data for statistical analysis. Outbreak investigation, disease surveillance, screening, bio monitoring, and conducting clinical trials are all public health functions.

a) Are deaths worldwide from AIDS, Tuberculosis, or Malaria increasing at a decreasing or increasing rate?

b) The New York Times recently reported that 20% of all U.S. households believe that vaccines are a cause of the increasing cases of autism. Would data collected show that vaccines are a significant cause of autism?

c) What is dengue (DEN GAY) fever? Is there cause for alarm in the U.S. and Florida? d) Is there a correlation between what state a person lives in and their risk for getting cancer? e) Is there a correlation between the number of TV sets per home and obesity rates? f) Has there been an increase in hate crimes from 2000 10 compared to earlier decades? g) Has there been an increase in bullying from 2000 10 compared to earlier decades? a) Has there been an increase in smoking from 2000 10 compared to earlier decades? h) Has there been an increase in teen pregnancy from 2000 10 compared to earlier decades? a) Has there been an increase in auto fatalities from 2000 10 compared to earlier decades? b) Have mandatory seatbelt laws saved lives? c) What day of the week are there more deaths recorded? d) Do states with lower speed limits have few fatalities? e) Is flying safer than driving? f) Towns with High schools that have earlier starting times report that students have more

accidents than students attending a school with a later starting time. Can you find data to verify this?

g) Do more car accidents happen on one particular day of the year such as the first day of Standard time after going off Daylight Savings time?

h) Should the minimum age for attaining a driver's license be increased? Should this be a national standard?

i) Do cameras at intersections stop people from running red lights and lower other traffic violations?

j) Many states have much harsher penalties than others for drunk driving. Do states with harsher penalties have fewer fatalities due to alcohol related accidents?

Medicine / Public Health Data Sources

o http://www.hivaidssurveillancedb.org/HIVDB/ Aids Surveillance Data Base:

o www.cdc.gov/nchs/ CDC National Center for Health Statistics Homepage o http://www.cdc.gov/az/ Centers for Disease Control topics A to Z (CDC) o http://www.cdc.gov/DataStatistics/ CDC Data & Statistics o http://www.americashealthrankings.org/ America’s Health Rankings o https://dawninfo.samhsa.gov/default.asp Drug Awareness Warning Network (DAWN): o http://progressreport.cancer.gov/ Cancer Trends Progress Report: o http://www.who.int/phe/health_topics/en World Health Organization (WHO) o http://www.nih.gov/ National Institute of Health (NIH) o http://www.cancer.gov/aboutnci/cis/page1 National Cancer Institute (NCI) o http://www.ncbi.nlm.nih.gov/pubmed PubMed.Gov o http://phpartners.org/health_stats.html Health Data Tools and Statistics: o http://mchb.hrsa.gov/mchirc/chusa/ U.S. Child Health Statistics:

o http://www.apa.org/topics/obesity/index.aspx American Psychological Association

Political Science

a) Do Exit polls accurately predict winners of elections? b) Has there been an increase in the percentage of eligible voters voting in presidential elections during 2000 10

compared to earlier decades? c) The World Series and the presidency-- During presidential election years, does the league that wins the World

Series determines which party wins the White House? d) Use secret ballots to survey student preferences for the next president of the United States. On half of the

ballots, list the likely Republican candidate first; on the other half, list the likely Democratic candidate first. e) There have been 5 election cycles in the last 60 years that had both a poor economy and a divided government:

1948, 1960, 2004 1992, and 2008. In all five elections, one party swept both the presidency and Congress. In four out of five cases, it was the party that controlled Congress — not the presidency — that did so. Interestingly the party completing the sweep in all five cases was the Democratic Party. Does this mean that maybe the Democratic Party has an inherent advantage over Republicans in difficult economic times?

Psychology

a) Texas executes the most people; has capital punishment reduced the amount of violent crime in Texas, or in any other U.S. state?

b) Do normally patient people become impatient behind the wheel? c) Is schizophrenia more common in men or women? d) Do men or women react to stress better? e) What are the effects on children whose parents push them in sports? f) Do certain children’s toys create social or emotional problems? g) Do students who finish an exam first score higher ?

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Education

a) Do school uniforms make a difference in achievement levels and / or better discipline? b) Are children smarter (or more socialized) because of the Internet? c) Do teenagers who take a “gap year” between high school and college do better or worse? d) In some European schools, fewer than 10% of students get as. Is there grade inflation in the U.S.? Why as many

As for Americans? e) Do children learn better in boys only and girls only schools? f) Does home schooling improve students’ scores on standardized tests?

Political Science / Psychology / Education Data Sources

o https://www.cia.gov/library/publications/the world factbook/ CIA World Fact Book o http://Fivethirtyeight.com http://fivethirtyeight.blogs.nytimes.com/ FiveThirtyEight is a polling aggregation o http://dawninfo.samhsa.gov/ Drug Awareness Warning Network (DAWN) o http://polisci.lsa.umich.edu/grad/comparative/data.htm o http://www.icpsr.umich.edu/icpsrweb/ICPSR/ InterUniversity Consortium for Political and Social Research: o http://politicaldata.com/Pages/Index.aspx Political Data Inc. o http://einstein.library.emory.edu/international_socsci.html International Statistical and Electoral Resources

Sports / Entertainment Research Questions:

Some possible project ideas could come from studying ambidexterity, various sports and games, especially darts, golf, basketball, archery and sharpshooting. Below are some general questions which could be investigated as a research project:

a) The World Series and the presidency-during presidential election years, does the league that wins the World Series determines which party wins the White House?

b) Is reality TV shows increasing at an increasing rate? Are Reality TV shows more popular in the North or South; East or West, or among what age groups?

c) Has the increase in ticket prices for a professional sports game prevented the average American family from attending a game?

d) Has the average professional sports players’ salary increased 10, 100 or more times the average American worker during the past several decades?

e) Has the average CEO’s (Chief Executive Officer) salary increased 10, 100 or more times the average American worker during the past several decades?

f) Can a player's batting average be predicted with reasonable accuracy from his batting average the preceding season?

g) Which sport is most played in the United States; or most played by region? h) Which sport is the most watched in the United States; or most watched by region?

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E. Projects Using Data Generated Or Collected By You

Sports / Entertainment Data Sources

a) http://www.stats.com/ Sports Data: b) http://baseball1.com/ website features baseball statistics beginning 1871. Includes player salary data c) http://www.cbssports.com/mlb/stats CBS Sports Data: fathom d) http://sabr.org/ Saber metrics e) NFL Quarterback Passer Rating Data http://www.dartmouth.edu/~chance/teaching_aids/data/NCAA.html f) http://www.usatoday.com/life/television/nielsen.htm Neilson Television Ratings:

Points to remember about generating your own data: You may learn more by analyzing data you have collected, than by analyzing data collected by another

person or organization. Rather than collecting information about an entire "population," random sampling allows one to

estimate population parameters using information obtained from a sample.

Collect additional data in case you need more. I.E. Collect height and weight in addition to Eye Color and Gender in case you end up needing more data to complete your project. You don’t have to use all of the data you collect, but it can be handy to have it and will be easier to collect in a “one stop shopping or collecting” of your data from the Web, surveys, polls, etc.

Analyzing your own data that you have collected will help you appreciate the P value. Obtaining a very small P value might make you think you have achieved results that are real. When a difference you obtained is large enough to be important but is not statistically significant you will learn the advantages of collecting more data.

You need to have a minimum of 40 pieces of data for your research project.

6 different data types and / or ways to process data statistically

1. Dichotomous Trial Data 2. Numerical Response Data 3. Categorical Data 4. Comparing two sample Data 5. Linear Regression Data 6. Chi Square Data

Dichotomous Trial Data

o Dichotomous (only yes / no; success / fail) Response Trials are research data collected or generated to try to make inferences about a larger population.

o These inferences can only be valid, if the trial unit results are obtained by random sampling. Random sampling means that the trials are independent and identically distributed.

o For a dichotomous response, trials are called “Bernoulli Trials”. Keep in mind that more data and more trials provide more accurate inferences.

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Dichotomous trials continued….

o Let the goal of the study determine the size of the trial; be careful not to make your number of trials too small.

o You can use as trials studying almost any event where the outcomes are limited to just two: o Success / failure; occurred / not occurred; presence / absence; disease / not diseased; etc. o Events such as: birth gender, ambidexterity, various sports and games, darts, golf, basketball,

archery and sharpshooting, are also good for dichotomous trial studies and research. o When you are analyzing your own data, you will begin to learn the importance of the number of

trials and data you collect. o Experimental trial units can involve people and the outcome of their behavior or response. o Trial units can also be virtually any objective outcome worth investigating.

Below are examples of dichotomous trials observed or obtained by students in math studies projects:

a) A student defined a trial to be her playing a B flat on her clarinet into a tuner. The tuner classified the note as sharp, flat, or perfectly in tune. A perfectly in tune note denoted a successful trial, while either of the other two classifications was labeled a failure.

b) A student defined a trial to be her father’s morning wait for the bus. If the bus arrived within two minutes of the scheduled time, the trial was a success; otherwise, it was a failure.

c) A trial was defined to be a live birth at a local hospital; female babies were successes and males were failures.

d) A trial was defined to be a bicyclist riding through a busy intersection. A rider with a helmet was a success and a rider without a helmet was a failure.

e) A student defined a trial to be rolling two small balls across the floor in her living room. A trial was a success if her dog, fetched the red ball and a failure if the dog fetched the blue ball.

Below are examples of trials and experiments used to obtain data for their research? Feel free to model your research question and project idea similar to one of the scenarios below:

a) A waitress wondered whether suggesting a specific appetizer upon greeting her customers would lead to an increase in the sales of appetizers. She was surprised to learn that —mentioning a specific appetizer decreased the sales of all appetizers.

b) A coffee cart offered two sizes, small and large. The salesperson wants to sell as many large coffees as possible. Some customers specified the size when they ordered. The worker experimented with the questions: “Would you like a large?” vs. “Would you like a small or a large?” To see if he could boost sales of large coffees. Which question would you guess would be statistically significantly superior in eliciting the sale of a large coffee?

c) An ice cream worker sold ice cream which could be served in a plain or a waffle cone. The store made a much larger profit on the waffle cones. For customers who did not specify the cone type in their order, it was found

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that the question, “Would you like a plain cone or a homemade waffle cone?” elicited significantly more sales of waffle cones than did the same question with the adjective “homemade” deleted.

d) A store purchased used compact discs from customers. The store owner wondered which of the following statements to the customer would be more effective. I will give you $X, or How does $X sound? (The value of X was appropriate for the number and quality of the compact discs offered for sale.) It was found that the first statement performed better (at getting an acceptance of the first offer) than the second, but that the difference barely missed achieving statistical significance. What do you think is meant by “statistical significance”?

e) At a university, and experimenter showed 25 graduate students part of an essay he said was written by “Jack McConnell, a student from Iowa.” He then showed 25 other college graduates the same essay, but said it was written by “Hsiao Ping Zhang, an international student from China.” When asked, “Do you detect any grammatical errors in this passage?” 64 percent who had read the Chinese student’s essay said yes, compared to only 20 percent who had read the Iowa student’s essay! This huge difference is highly statistically significant.

f) An experimenter visited a minimum security federal prison camp to obtain her study subjects who were first time nonviolent offenders. The first version of her question read: The prison is beginning a program in which inmates have the opportunity to volunteer for community service with developmentally disabled adults. Inmates who volunteer will receive a sentence reduction. Would you participate? The second version was the same, except that there was no mention of sentence reduction. The experimenter was surprised to learn that her data revealed that the second version received a much higher proportion of yes responses than the first version, but the difference did not quite achieve statistical significance. (Of course you cannot visit a prison, but maybe this scenario will provide you with some other idea…)

g) A novice golfer wondered whether she was more effective at hitting a golf ball from a fairway lie with a 3 wood or with a 3 iron.

h) A member of the university varsity soccer team had two games per week, every Friday evening and Sunday morning. She wondered whether she played better in the evening or morning.

i) A softball player and wanted to investigate whether the type of bat, aluminum or wood, influenced how far she could hit a pitched ball.

j) Students wanted to investigate whether having a car’s windows open or closed influenced the time required to accelerate from 40 to 65 miles per hour. (This one is not recommended for obvious reasons…)

k) A study can be performed a study to investigate the effect of temperature on the growth of a plant, flower, or fungus.

l) A competitive swimmer could perform a study to compare two methods of starting a freestyle swimming race. m) A punter on the varsity football team could perform a project to estimate how much farther he could punt the

ball with two steps (before kicking) rather than one step. Or, the “hang times” for one step or two steps could be investigated.

Linear Regression:

Go to a local grocery store and collect these data for at least 25 or more breakfast cereals: cereal name; grams of sugar per serving; and the price per ounce (or gram). If the store you select does not have at least 25 breakfast cereals, then collect data from another store too. Use these data to estimate the simple regression model with price as the dependent variable and sugar as the explanatory (Independent) variable.

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Numerical Response Data Projects

With numerical response trials and projects, pictures and graphs can be drawn and made of the data. Most projects with a numerical response are concerned with the center of the distribution; either larger or smaller is better. The next two projects provide examples in which spread is more important than center. The first project is an example that deals with variation from a fixed target and the second deals with the more common statistical problem of variation without a fixed target.

Numerical response data continued…

a) Two dart players had a contest to see who could hit the “20 wedge” the most. Each person attempted 78 throws, with each toss aimed at the 20 wedge. A response of 0 was noted if the throw hit the target wedge of 20. If the throw landed one wedge to the right of 20, the response was +1; if it landed two wedges to the right of 20, the response was +2, and so on. Darts that landed to the left of 20 gave responses of 1, 2, and so on, in the analogous manner. These data contained more information that only who was the better player. One player was better at hitting the 20, by a score of 36 to 10, and his mean response was 0.31. The second player’s mean response was 0.65. Since both numbers were positive, this indicates both had a tendency to shoot to the right. Another telling statistic is that one player’s mean absolute response was 0.62, and the second player’s was 1.71, which shows a substantial difference in variation.

b) A golfer wanted to compare the distributions of the distance obtained when hitting a golf ball with two seven irons; one made of steel and one of graphite. In golf, consistency with a seven iron is more important than distance; if you want to hit the ball farther, use a six iron. By examining dot plots, histograms, and various measures of spread, this project concluded that there was no substantial difference in the spreads of the two distributions.

Categorical Data Projects

a) Do comparisons of almost anything by randomly asking 15 male students and 15 female students to find differences or similarities in likes or dislikes. For example: To find out if as many males are fans of Lady Gage’s music as female students, or how many males vs. females watch Glee (or some other show)

b) Ask subjects to obtain 5 of the same things that are eatable/drinkable such as 5 donuts, 5 water bottles (the water inside them is what’s needed obviously), or 5 piece of candy. Please do not uses anything that is really small like one Skittle from a bag a small, fun size pack works well. Make sure they are all the same thing (5 fun size Skittles as opposed to 4 fun sizes and one giant bag). Then, eat/drink one at a time until you finish all five and after you eat one of them, give me your ranking from 1 10 on how satisfying it was. Example: 1st 9; 2nd 8; 3rd 3; 4th 9; 5th 10 be sure to eat/drink them all at the same time and take no breaks or other substances with them.

c) Ask 30 people to tell you when 30 seconds has elapsed, perhaps offering a prize if they are within 1 second. Think of a way to conduct this experiment that avoids this potential problem: if you time the 30 seconds by looking at your watch, the subject may be able to draw inferences from your facial expressions. Do your data indicate that people are more likely to underestimate or overestimate the passage of time?

d) People experiencing an earthquake often grossly overestimate how long the quake lasts; for example reporting that a 6 second quake lasted 30 seconds. Show a random sample of people some memorable event, such a snippet of loud music or you dancing, and then ask them how long this event lasted. Do your data indicate that people are more likely to underestimate or overestimate the how long the event lasted?

Chi square Tests for Categorical Data (Chi Squared 2 )

a) Administer the following four tests to at least 50 subjects, and then apply a chi square test to the six possible pairs of tests: a with b, a with c, and so on:

I. Ask the subject to stand with his or her back to you. Then ask the subject to jump around in a single motion to face you. Record whether the person jumps clockwise (pushing off with a dominant left foot) or counterclockwise (pushing off with a dominant right foot).

II. Ask the subject to look at an object 10 feet away through a tube made with the hands held a foot in front of his or her face. Close or cover first one eye and then the other and record whether the subject can still see the object through the tube when the left eye is open (left eye dominance) or when the right eye is open (right eye dominance).

III. Ask the subject to put his or her hands together behind the head, with the fingers interlaced. Record whether the thumb on the bottom (the dominant thumb) is from the left or right hand.

IV. Ask the subject whether he or she is left handed or right handed.

b) The nine positions on a baseball team can be divided into four categories: pitcher, catcher, the four infielders,

r

he obvious gender differences, they most resemble their

mputer software to simulate 1,000 spins of a roulette wheel that has 18 red slots, 18 black slots, and 1 green slot. Record the fraction of the spins that are red after 10, 100, and 1,000 spins. Repeat this experiment

men's and women's T shirts.

c) Would you bet $10 on the flip of a coin if you stood to win $20? (You have a 50% chance of losing $10 and compare the prices at stores in two

the door on the north side of building." From an inconspicuous location, observe how many people ignore the sign and use the main entrance and how many people do not use the main

b

and the three outfielders. Collect all the data you can on major league baseball managers and test the null hypothesis that, among those managers who played baseball, the probabilities of having played in these fou categories are 1/9, 1/9, 4/9, and 3/9, respectively.

c) Ask 100 randomly selected students if, aside from t iological mother or father. (Evolutionary psychologists suggest that people are more likely to say that a child

resembles the father—apparently so that the father will be more likely to protect and care for the child.) For each gender, test the null hypothesis that p = 0.5. (Alternatively, this can be done as a female/male chi square test.)

d) Use co

100 times and then use three box plots to summarize your results.

Comparing Two Samples

a) Compare the prices of

b) Compare the prices of men's and women's shaving cream

and a 50% chance of winning $20.) Select a grocery store chain different areas of town.

d) Post a sign on the main entrance to a campus building requesting the use of a less convenient entrance; for example, "Please use

entrance. Compare the behavior of students and professors or males and females. Try to pick a building and time when traffic is light, so that large numbers do not try to enter simultaneously.

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Simple Mathematics Process

Simple Mathematical Processes

F.

percentages areas of plane shapes linear and quadratic functions bar charts, pie charts mean and standard deviation simple probability frequency distribution grouped frequency distribution relative frequency distribution cumulative frequency distribution measures of central tendency frequency table joint, marginal, & conditional probability table standard error of the sample mean

The primary math to be used for your project is Statistics, which is why this course will cover Stat first. begin Statistics. Basic Statistics, such as entering data into x and y lists in

the calculator and generating scatterplots, histograms, and cumulative frequency tables and charts are considered simple math processes. Use of: Standard Deviation, Pearson Product Moment Calculation,

Only Algebra II is required to

2 (Chi Squared) and some other techniques to be studied are sophisticated math processes. To earn a

perfect mark of 5 for Criteria C, or a perfect score for your project, you will need to use two of these

processes, including linear regression and 2 (Chi Squared).

hey draw a scatter diagram and it is clear from the diagram that there is no correlation then it is ok if they calculate the correlation coefficient to verify that fact but it is not relevant to calculate the regression line. Project Math can also be: Trigonometry, Probability, Linear, Quadrati

If t

c, Power, and other regressions.

approved by me prior to your using them.

ur research question.

I must check your math processes—so you must come to me with the data already in lists in your calculator. Calculators are assigned to individual students.

Surveys must be Data obtained from academic, scientific, or industry internet sources is acceptable You must write minimum of one good quality paragraph for each project related math process—

explaining the relevance of the process towards answering yo

G. Sophisticated Math Processes

Sophisticated Mathematical Processes compound probability volumes of pyramids and cones analysis of trigonometric functions analysis of exponential functions Optimization statistical tests including: (below) linear regression Chi square "r" value or Pearson Product Moment Correlation Population mean Sample mean Variance Population variance Sample variance hypothesis test

2 Pearson Product Moment Calculation,Use of: Standard Deviation, (Chi Squared) and some other

studied are sophisticated math processes. To earn perfect mark of 5 for Criteria C, r a perfect score for your project, you will need to use two of these processes, including linear

techniques to be a o

regression and 2 (Chi Squared).

If you draw the scatter diagram and it seems that there is some correlation then you can continue to find r and, if the correlation is strong enough, then you may calculate the regression line and use it to count as one of your sophisticated processes. If you do not dra a scatter graph, w then the relevancy of a regression line will depend on the value of r.

nding by explaining what that r value indicates. Strive

ion calculations and the Pearson’s product moment correlation coefficient of “r”

5 in Criterion C.

you are intending to use the equation

Other words, if you simply just write down the value of r from your GDC then this will be graded as a simple process only.

Always try to add the idea of showing understa to keep things in context and don’t get carried away with equations and formulas while forgetting about the actual subject of your project.

Both the linear regress or PMCC calculation are considered sophisticated processes.

Linear Regression and Pearson Product Moment Correlation (PMCC) are 2 separate sophisticated processes so they can allow for a mark of

However the key word at this level is also "relevant". The calculation of the regression line is ONLY relevant if the R value calculated shows a strong correlation and for modeling, extrapolating, and conveying information, association, and causation (cause and effect).

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17

Criteria A: Produces a title, a clear statement of the task and a clear description of the plan.

The plan need not be highly detailed, but must describe how the task will be performed.

3. Prepare a clear description of the plan; i.e. what math processes will you use to try and

th

ob del or by experiment or conducting trials. Mathematic ssembled from outside sources. ..

includes data that is collected empirically or assembled from outside

or for obtaining your data whether you are generating

your own or collecting it from already established sources. or observation, describe your

:

a you will use; what is it measures 3. Identify the independent and dependent variable (if it’s two variable data)

to an Excel spreadsheet; assembled in rella. Remember, collected

sufficient in both

H. CRITERIA A & B ROUGH DRAFT ASSSIGNMENT DUE November 18th

1. PROVIDE A TITLE (SEE EXAMPLES SECTION K) 2. Produce a clear statement of task (SEE SAMPLES IN SECTION K)

demonstrate what result or prediction or hypothesis?

Criteria B: (along with criteria A) is due November 18 . “In this context, generated measurements include those that have been generated by computer, by

servation, by investigation, by prediction from a mathematical mo al information includes data that is collected empirically or a