Chapter 9 Probability & Statistics

May 30, 2012

Chapter 9Probability & Statistics

9.1 Probability in Society

Probability refers to the likelihood that something will occur.

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A probability of 40% can be expressed as

4 out of 10

4 / 10

0.4

or

or

9.1 Probability in Society

When you flip a coin, there is a 0.5 probability the coin will land heads up.

9.1 Probability in Society

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theoretical probability - the # of favorable outcomes written as a fraction of the total # of possible outcomes.ex. rolling dice, picking a card, flipping a coin.

experimental probability - the probability of an event calculated from experimental results.ex. weather predictions

subjective probability - prediction not based on probability (a "feeling")ex. your lucky number

9.1 Probability in Society

9.1 Probability in Society

How do assumptions affect probability? (p.426 Example 2)

Using probability to support opposing views (p.426 Example 3)

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Car insurance for teenagers is more expensive than for adults because the probability of an accident is greater for teenager drivers. What assumptions is an insurance company making when it charges a teenager driver more for insurance?

9.1 Probability in Society

Assign pg. 427- 429

# 3, 4, 5, 6, 9, 10, 11,14,17

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9.2 Potential Problems with Collecting Data

Don't you think students are working too much because of the large amount of homework assigned?

What are the problems with these questions?

How large is this textbook?

What is your favorite choice of music: rock, pop or country?

1. Bias

3. TimingWhen the data is collected, it could lead to particular results.

Ex. If the Oilers are in the playoffs, or on a winning streak may get different results on the arena question than if they are not.

The Question Influences responses in favour of, or against the topic of data collection.

Ex. Don't you think there should be a downtown arena?

2. Cultural SensitivityCultural sensitivity means that you are aware of other cultures. You must avoid being offensive and asking questions that do not apply to that culture.

Ex. Asking muslims what their favorite way of cooking pork is not appropriate. It doesn't apply to them.

There are several problems with data collection:

9.2 Potential Problems with Collecting Data

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4. Use of LanguageThe use of language in a question could lead people to a particular answer.

Ex. Don't you think the price of a downtown arena would be too high? or Do you think the price of the arena is reasonable...

5. EthicsEthics dictate that data collected must not be used for purposes other than those told to the participants.

Ex. Asking a season ticket holder about their 2nd, 3rd, 4th favorite teams in the league in order to get a sense of the type of team fans would like to see in Edmonton, but then using that information to try to sell tickets to those games to the person surveyed.

The cost of collecting data must be taken into account.

Ex. If you need to pay for printing or for people to collect data it might be too expensive.

6. Cost

9.2 Potential Problems with Collecting Data

7. PrivacyIf the topic of data collection is personal a person may not want to participate or may give an untrue answer on purpose. Anonymous surveys may help.

Ex. People may not participate if they have to weigh themselves in front of others.

8. Time

The time needed for collecting data must be considered.

Ex. A survey that takes an hour to complete may be too long for most people. Not many people will take the survey.

CanadianBlood

Services

9.2 Potential Problems with Collecting Data

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For each question explain the problem and the effect it would have on the result if any:

1. A survey was conducted to find what classes MCHS students liked the best. The question was asked: Don't you like Math class the best?

2. A corporation polls 300 students at school to determine their favorite pop brand. After getting the results the price of the most popular drink goes up by 25cents in the pop machine.

3. A survey is conducted on how well you like the school. Students are polled during the annual Christmas dinner.

4. Students are asked face to face, by their teacher, whether they do drugs.

9.2 Potential Problems with Collecting Data

Mr. Korotash, Mr. Bodnar, and Mr. Fidler want to open a small hockey card shop in St. Albert. To ensure its the best place to open a store he wants to survey all the residents of St. Albert. Why might this be problematic for him?

9.2 Potential Problems with Collecting Data

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Sears Canada wants to find out if there is a relationship between income and the amount people spend on Christmas gifts.

Identify problems that they may encounter and how they could deal with the problem.

9.2 Potential Problems with Collecting Data

Assignment pg. 435 # 3, 5, 6, 7, 8, 9

9.2 Potential Problems with Collecting Data

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9.3 Using Samples and Populations to Collect Data

Coin flipping Demo

Frequency of flipping heads when coin is flipped 10 times:

Frequency of flipping heads when coin is flipped 20 times:

Frequency of flipping heads when coin is flipped 30 times:

Pre - Reading Exercise

What is your understanding about the following:

~ population~ census~ sample

9.3 Using Samples and Populations to Collect Data

Read page 438"Connect" andwrite your owndefinitions for

population, census,and sample

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Example 1To determine the average number of siblings of his classmates, Bailey surveyed each person in his class.

Explain why a population was surveyedinstead of a sample.

9.3 Using Samples and Populations to Collect Data

Example 2:

Every 5 years, Statistics Canada conducts a census. One question in the survey is used to determine the ages of the people in each household.

Explain why a population was surveyedinstead of a sample.

9.3 Using Samples and Populations to Collect Data

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Paired Reading ActivityRead through Examples 2 and 3 (pg. 439) Discuss your ideas, reasons, and thoughts for each question before going to the Solution. When finished discussing, read through the solutions to see how close their responses were, and what ideas arise that you may not have thought of.

10 minute activity

9.3 Using Samples and Populations to Collect Data

Assignment

pg. 440 # 1, 4, 5, 6, 8, 9, 10.

Next day - Mid Unit Quiz

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9.4 Selecting a Sample

In Partners, read & discuss "Investigate" on page 445

Complete the following web in your notebook with the different sampling methods. Create your own example, rather than the one from the book.

Sampling Methods

Simple Random SamplingEach member of a population has an equal chance of being selected

Ex. 600 phone numbers are randomly generated from a list all Morinville phone numbers

Stratified Random Sampling Some members from each group of the population are randomly selected.

Ex. 5 students, 5 teachers, and 5 parents are selected randomly about a new school program

Systematic or Interval Sampling Every n'th member of the population s selected

Every 100th passenger is selected to complete a survey about air travel

Cluster Sampling Every member of each randomly chosen group of the population is selected

Ex. Grade 3, 6, 9, 12 PAT examsEx. All Grade 10 students complete school survey

Self-Selected Sampling Only members who are interested and volunteer will participate

Ex. Radio station phone-in polls / "question of the day"

Online surveys to which are there are not codes / passwords

Convenience Sampling Only members of the population who are convenient to include are selected

Ex. Asking people on the bus what they think of bus pass prices

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9.4 Selecting a Sample

Which sampling methods are least likely to produce valid conclusions? Explain

Which sampling methods are most likely to produce valid conclusions? Explain

P. 448 - 449 #3,4,7,8,12a

9.4 Selecting a Sample

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9.5 Designing a Project Plan

5 steps:

1) Prepare a question - avoid bias, be culturally sensitive, and make anonymous if personal.

2) Identify the population and choose a sample if necessary- Ensure sample represents population and consider time and cost involved.

3) Collect the Data- Consider the timing of your data collection

4) Analyze and display the data- Choose an appropriate display for the data (ex. table or graph) and the type of graph

5) Evaluate results based on validity of data.

9.5 Designing a Project Plan

In groups of two think of a survey question that the school, the town, the province, or a business might like to ask. Design a project plan.

Point form is fine. You will share your project plan with the class.