Welcome to MM207 Survey of Mathematics! Dr. Jami Stone Me on Skype: jamaleebs Cell phone: (402)...

Welcome to MM207 Survey of Mathematics!Dr. Jami Stone

Me on Skype: jamaleebsCell phone: (402) 613-0136Flex Seminar Times:

Wednesdays from 12PM to 1PM ET, with Instructor: Tatiana Scott, AIM Name: tessverseau, E-Mail: [email protected]

Wednesday from 8PM to pPM ET, with Instructor: LaTriece Tanksley, AIM Name: tank777, E-Mail: [email protected]

Thursdays from 9PM to 10 PM, with Instructor: Jami Stone,AIM Name: jamijstone, E-Mail: [email protected]

Sundayss from 8PM to 9PM ET, with Instructor: Bob Lockwood, AIM Name: drboblockwood, E-Mail: [email protected]

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mailto:[email protected]




There are lots of topics each week, we can’t cover them all in Seminar, but I do cover a bunch of them. If I don’t cover it, you will have to do on your own, attend another seminar or email to schedule an Office Hour (SKYPE)

At 10PM, Seminar is over, but I am happy to continue as long as people stay. I go over additional topics for the week, and answer additional questions.

Please, post to Doc Sharing or the Webliography any files or sites that you find helpful, so your classmates can make use of them too!

Remember Active On-Topic Participation for the entire hour is an important part of your Seminar Grade! Answer questions from me or your classmates, ask relevant questions, give further clarification!

WARNING: Off-topic chatting during Seminar is distracting to me and to other students. Please keep it to a minimum, otherwise we may not get through many topics during our time together

2Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter.

Put "?" in front of Questions so it is easier to see them.

Typing Math

Use:* for multiplication (shift 8), x is for variables/ for division (next to right shift key)^ for exponents (shift 6), may need ( & ) to clarify alsoonly one equals per line (on DB)only one step of a problem per line (on DB)

Symbols are on DB under Ω

Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 3

1.1

What is/are Statistics

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Two Definitions of Statistics

• Statistics is the science of collecting, organizing, and interpreting data.

• Statistics are the data (numbers or other pieces of information) that describe or summarize something.



How Statistics WorksWhat is the Goal of Research?

The population in a statistical study is the compete set of people or things being studied.

Population parameters are specific characteristics of the population.

How Statistics WorksWhat Actually Gets Studied?

• A sample is a subset of the population from which data are actually obtained.

• The actual measurements or observations collected from the sample constitute the raw data.

• Sample statistics are characteristics of the sample found by consolidating or summarizing the raw data

• The margin of error in a statistical study is used to describe the range of values, or confidence interval, likely to contain the population parameter.



EXAMPLE: Unemployment Survey

The U.S. Labor Department defines the civilian labor force as all those people who are either employed or actively seeking employment. Each month, the Labor Department reports the unemployment rate, which is the percentage of people actively seeking employment within the entire civilian labor force. To determine the unemployment rate, the Labor Department surveys 60,000 households. For the unemployment reports, describe the:

a. population b. sample c. raw data d. sample statistics e. population parameters

a. population:The population is the group that the Labor Department wants to learn about, which is all the people who make up the civilian labor force.

b. sampleThe sample consists of all the people among the 60,000 households surveyed.

c. raw dataThe raw data consist of all the information collected in the survey.


Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them.

d. sample statisticsThe sample statistics summarize the raw data for the sample. In this case, the relevant sample statistic is the percentage of people in the sample who are actively seeking employment.

e. population parametersThe population parameters are the characteristics of the entire population that correspond to the sample statistics. In this case, the relevant population parameter is the actual unemployment rate.


Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them.

Basic Steps in a Statistical StudyStep 1: State the goal of your study precisely; that is, determine the population you want to study and exactly what you’d like to learn about it. Step 2: Choose a sample from the population. Step 3: Collect raw data from the sample and summarize these data by finding sample statistics of interest.Step 4: Use the sample statistics to make inference about the population.Step 5: Draw conclusions; determine what you learned and whether you achieved your goal.

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1.2

Sampling

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Definitions• A census is the collection of data from every member of

a population• A representative sample is a sample in which the

relevant characteristics of the sample members are generally the same as the characteristics of the population.

• A statistical study suffers from bias if its design or conduct tends to favor certain results.



Summary of Sampling MethodsKeep in mind the following three key ideas:• A study can be successful only if the sample is representative of the population.

• A biased sample is unlikely to be a representative sample.

• Even a well-chosen sample may still turn out to be unrepresentative just because of bad luck in the actual drawing of the sample.



Types of Sampling• A random sampling occurs if a sample is

drawn in such a way that each time an item is selected, each item has an equal chance of being drawn.

• When a sample is obtained by drawing every nth item on a list or production line, the sample is a systematic sample.

• A cluster sample is sometimes referred to as an area sample because it is frequently applied on a geographical basis, or location.


Types of Sampling continued

• Stratified sampling involves dividing the population by characteristics called stratifying factors such as gender, race, religion, or income.

• Convenience sampling uses data that are easily or readily obtained, and can be extremely biased, and so not a representative sample.


Example: Identifying Sampling Techniques

a. Participants are selected using a random number generator.

b. Students at an elementary school are classified according to their present grade level. Then, a random sample of three students from each grade are chosen to represent their class.

c. Every sixth car on highway is stopped for a vehicle inspection.


Example: Identifying Sampling Techniques continued

d. Voters are classified based on their polling location. A random sample of four polling locations are selected. All the voters from the precinct are included in the sample.

e. The first 20 people entering a water park are asked if they are wearing sunscreen.


Solution:a) Random d) Clusterb) Stratified e) Convenience c) Systematic


1.3

Types of Statistical StudiesLots of Definitions, more in textbook.



Basic Types of Statistical Studies

1. In an observational study, researchers observe or measure characteristics of the subjects but do not attempt to influence or modify these characteristics.

2. In an experiment, researchers apply some treatment and observe its effects on the subjects of the experiment.



Definitions• The subjects of a study are the people, animals (or other living

things), or objects chosen for the sample; if the subjects are people, they may also be called the participants in the study.

• A variable is any item or quantity that can vary or take on different values.

• The variables of interest in a statistical study are the items or quantities that the study seeks to measure.

• When cause and effect may be involved, an explanatory variable is a variable that may explain or cause the effect, while a response variable is a variable that responds to change in the explanatory variable.


The treatment group in an experiment is the group of subjects who receive the treatment being tested.

The control group in an experiment is the group of subjects who do not receive the treatment being tested.

In most cases, it is important to choose the members of the two groups by random selection from the available pool of subjects.

A study suffers from confounding if the effects of different variables are mixed so we cannot determine the specific effects of the variables of interest. The variables that lead to the confusion are called confounding variables.


Treatment and Control Groups

More Definitions• A placebo lacks the active ingredients of a treatment being tested

in a study, but looks or feels like the treatment so that participants cannot distinguish whether they are receiving the placebo or the real treatment.

• The placebo effect refers to the situation in which patients improve simply because they believe they are receiving a useful treatment.

• An experimenter effect occurs when a researcher or experimenter somehow influences subjects through such factors as facial expression, tone of voice, or attitude.

• In a meta-analysis, researchers review many past studies. The meta-analysis considers these studies as a combined group, with the aim of finding trends that were not evident in the individual studies.


1.4

Should You Believe a Statistical Study?

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Some Definitions

Peer review is a process in which several experts in a field evaluate a research report before the report is published.

Selection bias (or a selection effect) occurs whenever researchers select their sample in a biased way.

Participation bias occurs any time participation in a study is voluntary.

A self-selected survey (or voluntary response survey) is one in which people decide for themselves whether to be included in the survey.

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Guideline 1: Identify the Goal, Population and Type of Study

Based on what you hear or read about a study, try to answer these basic questions:• What was the study designed to determine?• What was the population under study? Was the population clearly and appropriately defined?• Was the study an observational study, an experiment, or a meta-analysis?



Guideline 2: Consider the SourceStatistical studies are supposed to be objective, but the people who carry them out and fund them may be biased.It is therefore important to consider the source of a study and evaluate the potential for biases that might invalidate the study’s conclusions.

Guideline 3: Examine the Sampling Method

A statistical study cannot be valid unless the sample is representative of the population under study.

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Guideline 4: Look for Problems in Defining or Measuring

the Variable of InterestResults of a statistical study may be difficult to interpret if the variables under study are difficult to define or measure.



Guideline 5: Watch Out forConfounding Variables

Often, variables that are not intended to be part of the study can make it difficult to interpret results properly.

Guideline 6: Consider the Setting and Wording in Surveys

Even when a survey is conducted with proper sampling and with clearly defined terms and questions, you should watch for problems in the setting or wording that might produce inaccurate or dishonest responses.

Dishonest responses are particularly likely when the survey concerns sensitive subjects.



Guideline 7: Check That Results Are Fairly Represented in Graphics or Concluding Statements

Even when a statistical survey is done well, it may be misrepresented in graphics or concluding statements.



Guideline 8: Stand Back and Consider the Conclusions

Ask yourself questions such as these:

• Did the study achieve its goals?

• Do the conclusions make sense?

• Can you rule out alternative explanations for the results?

• If the conclusions make sense, do they have any practical significance?

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Welcome to MM207 Survey of Mathematics!Check the Roster under the Chat area for your Name, otherwise there may be delays in getting credit!PDF of this PPT & others: http://www.ramshillfarm.com/Math/Math207/Unit_1.html Extra Materials by me: http://www.ramshillfarm.com/Math/Math207/index.htmlHelpful Bookmarks: http://delicious.com/TamaraEysterGood Free PDF Printer: Primo PDFMe on Facebook: http://www.facebook.com/tinksbellMM207 Group on Facebook: http://www.facebook.com/groups/MM207/ Flex Seminar Times:

Thursdays from 11AM to 12PM ET, with Instructor: Tamara E, AIM Name: TamaraEyster, E-Mail: [email protected]

Thursdays from 7PM to 8PM ET, with Instructor: Anne Franklin, AIM Name: annerfranklin, E-Mail: [email protected]

Mondays from 6PM to 7PM ET, with Instructor: Rudilee Gabel, AIM Name: rdgabel11, E-Mail: [email protected]



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Welcome to MM207 Survey of Mathematics! Dr. Jami Stone Me on Skype: jamaleebs Cell phone: (402)...

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