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7-8. Populations and Samples. Warm Up. Problem of the Day. Lesson Presentation. Course 2. 7-8. Populations and Samples. Course 2. Learn to compare and analyze sampling methods. 7-8. Populations and Samples. Course 2. Vocabulary. population sample random sample convenience sample

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7-8

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7-8

Populations and Samples

Warm Up

Problem of the Day

Lesson Presentation

Course 2

7-8

Populations and Samples

Course 2

Learn to compare and analyze sampling methods.

7-8

Populations and Samples

Course 2

Vocabulary

population

sample

random sample

convenience sample

biased sample

7-8

Populations and Samples

Course 2

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.

7-8

Populations and Samples

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

Course 2

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.

7-8

Populations and Samples

Course 2

Additional Example 1: Analyzing Sampling Methods

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

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

7-8

Populations and Samples

Course 2

Check It Out: Example 1

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

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

7-8

Populations and Samples

Course 2

A biased sample does not fairly represent the population and systematically favors certain outcomes. For example, 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.

A voluntary response sampling occurs when people themselves choose to respond to a general appeal. Often, people that volunteer to respond to questions have strong opinions, often negative ones, that may not represent the population well.

7-8

Populations and Samples

Course 2

Additional Example 2: Identifying Potentially Biased Samples

Determine whether each sample may be biased. Explain.

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.

7-8

Populations and Samples

Course 2

Check It Out: Example 2

Determine whether each sample may be biased. Explain.

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.

7-8

Populations and Samples

Course 2

Additional Example 3: Verifying Claims Based on Statistical Data

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.

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

Students attending sample # of Students sampled

Students attending Student Population

=

7-8

Populations and Samples

Course 2

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.

Multiply.

9000 = 25x

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.

7-8

Populations and Samples

Course 2

Check It Out: Example 3

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.

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

=

7-8

Populations and Samples

Course 2

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.

Multiply.

9600 = 40x

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.