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Populations & SamplesJanuary 04, 2013

+Riddle Me This..

What is in seasons, seconds, centuries, and minutes but not in decades, years, or days?

The letter “n” seasoNs secoNds ceNturies miNutes

+Kick Off

Evaluate the expression using the correct order of operations.

9 + 3(4 - 2) – 8 / 2 11

+Essential Question

How can I compare and analyze sampling methods?

BrainPop: Statistics

+Objective

Learn to compare and analyze sampling methods.

+Vocabulary

Population The entire group of objects or individuals considered for a survey

Sample A part of a population

Random Sample A sample in which each individual or object in the entire population

has an equal chance of being selected

Convenience Sample Sampling the most available subjects in a population to obtain quick

results

Biased Sample A sample that does not fairly represent the population

+

In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to verify claims such as these, the elk population had to be tested.

When information is gathered about a group, such as the elk in North America, the entire group is called the population. Because testing each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample.

Populations and Samples

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For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen. A convenience sample is based on members of the population that are readily available, such as 30 elk in a wildlife preservation area.

A random sample is more likely to be representative of a population than a convenience sample is.

Helpful Hint

Populations and Samples

+

Determine which sampling method will better represent the entire population. Justify your answer.

Additional Example 1: Analyzing Sampling Methods

Sampling methodMaria surveys only the band students she knows personally.

Results84% want blue uniforms

Jon writes each band student’s name on a card. He questions those students whose name he draws.

61% want blue uniforms

Jon’s sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.

Populations and Samples

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Determine which sampling method will better represent the entire population. Justify your answer.

Check It Out: Example 1

Sampling methodFerdinand surveys every other swimmer on the team.

Results72% want practice early

Anna-Maria questions the swimmers who are in her Biology class.

50% want practice early

Ferdinand’s sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.

Populations and Samples

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A biased sample does not fairly represent the population. A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.

Populations and Samples

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Determine whether each sample may be biased. Explain.

Additional Example 2: Identifying Potentially Biased Samples

A. The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council.

The sample is biased. The supporters may have different ideas than those not at the rally.

B. The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances.

The sample is random. The students all have a chance to respond.

Populations and Samples

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Determine whether each sample may be biased. Explain.

Check It Out: Example 2

A. The owner of a record shop surveys only customers over the age of 18 who shop at his store.This is not random. Customers under the age of 18 do not have a chance of being chosen.

B. The teacher writes the name of each student on a piece of paper and questions the students whose names are drawn.

This sampling method is random. Each student has an equal chance of being chosen.

Populations and Samples

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A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principal’s estimate is likely to be accurate.

Additional Example 3: Verifying Claims Based on Statistical Data

Set up a proportion to predict the total number of students that will attend.

Students attending sample # of Students sampled

Students attending Student Population

=

Populations and Samples

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Additional Example 3 Continued

Let x represent the number of actual students attending the band festival.

6 25

x 1500

=

6 • 1500 = 25 • x The cross products are equal.

9000 = 25x Multiply.

9000 25

25x 25

= Divide each side by 25 to isolate x.

360 = x

The estimate is not accurate because the data shows that 360 students are likely to attend.

Populations and Samples

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The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owner’s estimate is likely to be accurate.

Check It Out: Example 3

Set up a proportion to predict the total number of students that will attend.

Employees surveyed for time off # of Employees surveyed

Employees asking for time off Total # of Employees

=

Populations and Samples

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Check It Out: Example 3 Continued

Let x represent the number of actual employees asking for time off.

8 40

x 1200

=

8 • 1200 = 40 • x The cross products are equal.

9600 = 40x Multiply.

9600 40

40x 40

= Divide each side by 40 to isolate x.

240 = x

The estimate is accurate because the data shows that 240 employees will ask for time off.

Populations and Samples

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a. A TV ratings service is surveying residents of Orlando who bought TVs in the last month about their favorite TV show.

b. A TV ratings service called residents of Orlando randomly selected from the phone directory to conduct a survey about their favorite show.

Lesson Quiz: Part I

b1. Determine which sample better represents the

entire population.

Populations and Samples

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2. Determine whether each sample may be biased. Explain.

Lesson Quiz: Part II

Biased; at other times of the day, customers may have different preferences.

a. A convenience store surveys customers one morning to determine what products they may like the store to stock.

b. Each student’s name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom representative.

Not biased; the sample is random.

Populations and Samples

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3. A local middle school has 2500 students. Morgan interviewed 75 of the students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly.

Lesson Quiz: Part III

1500

Populations and Samples

+Let’s Practice

With your elbow partner, complete 7-8 Reteach and 7-8 Reading Strategies.

If you finish, raise your hand for me to check your work. If your work is accurate, you may begin on your homework.

HW: WB 7-8, page 65

Last five minutes: Continue to work while I stamp agendas.

+Essential Question

What factors affect the outcomes of a survey or study? Why is this important to me?

How do you select a valid sample to survey or study?

+Frameworks Task

Individually and silently, work for 10 minutes on the Is It Valid? Task provided.

After 10 minutes, you may discuss with your elbow partner for an additional 10 minutes.

If needed, you will be given 5 additional minutes of individual work time to complete the task.

Write your name on the paper and turn in to the basket.

+Puzzles, Twisters, & Teasers

1. Tyler surveys 60 people at a high school football game to find out which high school sports team is most popular.

O A

biased not biased

2. A computer manufacturer randomly calls 150 people who called its help line and surveys them to determine if they were satisfied with the help they received.

M N

biased non biased

+Puzzles, Twisters, & Teasers

3. Margie surveys 12 of her friends to determine what percentage of students participate in after-school clubs.

F D

random sample convenience sample

4. Tamira surveys 50 riders on one commuter train to determine whether riders on all trains in the system think that the on-time performance is adequate.

K A

biased non biased

+Puzzles, Twisters, & Teasers

5. Sam calls every sixth student on a high school attendance list and surveys the students to determine their favorite subject.

M R

random sample convenience sample

Write the circled letters above the problem numbers to solve the riddle.

What is the difference between dinosaurs and dragons?

Dinosaurs ____ ____ ____ ____ T S ____ ____ ____ E.

3. 1. 2. 1. 5. 1. 4.

+Homework

For the rest of the period, you may work quietly with your elbow partner on your homework.

HW: 7-8 Problem Solving

Last five minutes: Continue to work while I stamp agendas.