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Introduction to Statistics

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Introduction to Statistics

Math 11

1-14-14

Important Information

No cell phones in class.

We have a class website. It is www.cfioritto.wordpress.com

Homework is given daily for each section and due on Tuesday.

Everyday starts with a warm up, goes to instruction, goes to break, goes to IC, finishes with quiz.

We take a test at the end of every chapter.

The final will be cumulative.

My grading scale is 20,20,20,40. Hw, Ic, and Quizzes are all 20% while tests are 40%.

Questions?

Lets get started.

- I am Mr. Fioritto.
- You are Math 11.
- We meet from 12:30-2:20 on T, Th.
- We will use the text Elementary Statistics 12th edition by Mario Triola.
- Mac lab attendance and assignments are mandatory.
- My email is [email protected]
- My phone number is 707-673-7592.
- Four absences will result in a drop.
- Cheating will result in a zero on the assignment when you are caught.

Warm Up

- The picture at the right is the preface of section 1-1. It is about the importance of surveys and understanding misleading results. The goal here is to understand that some surveys have valid results and some do not.
- 1. From the bar graph, about how many times as many people said yes as those who said no?

Warm Up continued

From the warm up

-Non zero graphs are misleading to the reader.

-Self selected samples distort results.

-Results like these are meaningless.

Warm Up continued

Every time you see a survey, poll, etc you must ask how were the results collected and how are they being presented?

Statistical studies with misleading results and/or flawed sample methods have results that may not be valid.

Some studies may have valid results but those results are not very practical or useful in everyday life.

Objectives

- Students will learn the PAC process.
- Students will identify misleading results.
- Students will check for statistical and/or practical significance.
- Students will use percentages.

Your Turn

State one of our objectives.

Definition

Data

Collections of information from observations.

Statistics

The science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

- Population –
- A population is the complete collection or all the data that are being considered.
- Sample –
A sample is a subset of members selected from a population.

- Census –
- A census is a collection of data from every member of a population.

Example

In a poll conducted by the Gallup corporation, 1013 adults in the United States were randomly selected and surveyed about identity theft. Results showed that 66% of the respondents worried about identity theft frequently or occasionally.

Gallup pollsters decided who would participate in the survey and they used a sound method of randomly selecting adults. The respondents are not a voluntary response sample, and the results are likely to be better than those obtained from the America Online survey discussed earlier.

A. Describe the population. B. Describe the sample.

Your turn

- In the previous example what do the data mean? What was the goal of the study?
- About how many people said yes?

Definition

- The PAC process

The PAC process is a generalized approach at how we do a statistical study.

P is for preparing

A is for analyzing

C is for concluding

Definition

- Preparing
- In planning a study we look at the context of the data, the source of the data and the sampling method used.
- The context of the data is found by asking what do the data mean? What is the goal of the study?
- The source is important so we know there is no bias or special interest.
- The sampling method is especially important since we need the sample to truly reflect the population.

Example

What do the data mean?

Assume that neither the source nor the sampling method were biased.

Your Turn

What is the goal of the study?

Assume that neither the source nor the sampling method were biased.

Definition

In the preparing phase we also consider sampling method. It is important that every study has a sound sampling method.

A common bad practice in statistical studies is to use a voluntary response sample which is a sample where respondents DECIDE whether or not they will participate.

A good example is an online survey where respondents choose whether or not they will click the button to participate.

Example

Your turn

A hip hop radio show broadcast in the city of Puddelton asked people to call in and express their opinions on the new mayor. Are the results likely to be representative of all adults in Puddelton? Of all listeners to the hip hop show? Why or why not?

Definition

- Analyzing
- In analyzing the data, we look at graphs of the data and use technology to obtain results that we may interpret.
- Some formulas are more simple than others and do not require technology.

In the analyzing phase there are potential pitfalls we must consider.

People commonly conclude that changes in one variable cause changes in the other variable when it does not.

Two variables that may seemed linked, like smoking and pulse rate.

However, Correlation is not causation.

Definition

Math 94 1-22-14

Definition

Example: The Children’s Defense Fund published Children Out of School in America where it was reported that among secondary school students suspended in one region that 67% were suspended at least three times. However, that figure is based on a sample of only three students.

Math 94 1-22-14

Definition

The way questions are worded can strongly affect the results.

When the question was asked as “Should the President have the line item veto to eliminate waste?” 97% said yes.

When the question was asked as“Should the President have the line item veto, or not?” 57% said yes.

Math 94 1-22-14

Definition

Occurs when someone either refuses to respond to a survey question or is unavailable.

People who refuse to talk to pollsters have a view of the world around them that is markedly different than those who will let pollsters into their homes.

Math 94 1-22-14

Definition

Because as a figure is precise like the example that said 241,472,385 people live in America, many people incorrectly assume that it is also accurate.

A precise number can be an estimate, and it should be referred to that way. It would be more accurate to say that about 240 million adults live in America.

Definition

Misleading or unclear percentages are sometimes used.

Example – Continental Airlines ran an ad claiming “We’ve already improved 100% in the last six months” with respect to lost baggage.

Does this mean Continental made no mistakes?

Definition

- Concluding
- In concluding we look at the results and determine if they have statistical and/or practical significance.

Definition

Statistical Significance

- A study has Statistical significance when a result is found that is very unlikely to occur by chance.
- Getting 98 girls in 100 births is statistically significant. It is unlikely to occur by chance.
- Getting 52 girls in 100 births is not statistically significant . It could easily occur by chance.

Definition

Practical Significance

- A study has Practical Significance when a result is found that is useful or meaningful.

Example

- In a test of the Atkins weight loss program, 40 subjects using that program had a mean weight loss of 4.6 pounds after one year.
- Determine if the study has statistical significance and if it has practical significance.

Example Continued

- The study has statistical significance. It is not likely that 40 people would try this and all lose weight in one year without it being effective.
- However, although 4.6 pounds is statistically significant, using common sense, it does not seem very worthwhile or meaningful. The study does not have practical significance.

1. A coach uses a new technique in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below.

Athlete A B C D E F G H

Before 115.2 114 116.4 119.8 110.9 112.4 111.5 117.3

After 112.9 112.7 114 120.6 109.1 109.1 107.9 113.4

Does the conclusion that the technique is effective appear to be supported with statistical significance?

Does the conclusion that the technique is effective appear to have practical significance?

2. A teacher was interested in knowing how much tax people pay in the United States. She selected a simple random sample of her friends and asked them about their taxes. Is this sample likely to be representative of all adults in the United States?

3. Describe at least one example of misleading results.

4. Create your own example using the terms sample and population.

5. What is the PAC process?