7-6 Populations and Samples Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

7-6 Populations and Samples

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpSolve.

n = –0.0625

1. 12 =

2. 8n = –0.5

3. n – 9 = –14

2 5

n 9

n = 1113 5

4. –16 = n – (–30)

n = –15

n = –46


Problem of the Day

Why are both products the same?26 51 = 1,326 39 34 = 1,326

26 51 = (2 13) (3 17);

39 34 = (3 13) (2 17);

They have the same factors: 2, 3, 13, and 17


MA.7.S.6.1 Evaluate the reasonableness of a sample to determine the appropriateness of generalizations made about the population.

Sunshine State Standards


Vocabularypopulationsamplerandom sampleconvenience samplebiased sample


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.


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


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

Additional Example 1: Analyzing Sampling Methods

61% want blue uniforms

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

Results84% want blue uniforms

Sampling methodMaria surveys only the band students she knows personally.

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


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

Check It Out: Example 1

50% want practice early

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

Results72% want practice early

Sampling methodFerdinand surveys every other swimmer on the team.

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


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.


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.


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.


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

=


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.


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

=


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.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


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.


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.


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 students


1. Determine which sample better represents the entire population.

A. 100 people exiting a football stadium are surveyed to find out the favorite game of the city residents.

B. 200 people of the city are randomly selected from the phone directory and surveyed to find out the favorite game of the city residents.

C. 150 members of a golf club are surveyed to find out the favorite game of the city residents.



2. Determine whether the sample may be biased. Explain.Smith surveys 35 people in the purchase department of his company to determine the favorite hobbies of the employees of the company.

A. Biased; the other employees may have other preferences.

B. Not biased; the sample is random.

C. Biased; the sample is random.



3. A machine produces 225,000 insulating washers for electrical devices per day. In a random sample of 200 washers, there were 4 defectives. Predict the number of defective washers produced by the machine per day.

A. 2,250

B. 4,500

C. 9,000

D. 22,500


Documents

7-6 Populations and Samples Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes