Holt CA Course 1

7-6 Populations and Samples

SDAP2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.Also covered: NS1.3, SDAP2.5

California Standards

Holt CA Course 1

7-6 Populations and Samples

Vocabularypopulationsamplerandom sample

Holt CA Course 1

7-6 Populations and SamplesIn 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to evaluate these claims, the elk population had to be tested.

A population is an entire group of objects or individuals that is considered for a survey. All of the elk in North America is an example of a population.

Surveying or testing every member of a large group can be difficult or impossible. Instead, researchers often study a sample. A sample is a part of the population.

Holt CA Course 1

7-6 Populations and Samples

For each situation, explain whether it makes sense to use a sample.

Additional Example 1: Deciding When to Use a Sample

A. The manager of a store wants to know the average age of the store’s customers.

The entire population is large. It would be difficult to find out the age of every customer. It does make sense to use a sample.

B. The manager of a store wants to know the average salary of the store’s 8 employees.

The entire population is small. It does not make sense to use a sample because every employee can be evaluated.

Holt CA Course 1

7-6 Populations and Samples

For each situation, explain whether it makes sense to use a sample.

Check It Out! Example 1

A. A veterinarian wants to know the average number of pets in her town.The entire population is large. It would be difficult to find out the number of pets in a town. It does make sense to use a sample.

B. The veterinarian wants to determine how many pets she can house in her 10 kennels.

The entire population is small. It does not make sense to use a sample because every kennel can be evaluated.

Holt CA Course 1

7-6 Populations and Samples

In a random sample, each member of the population has an equal chance of being selected. A random sample is more likely to be representative of a population than samples that are chosen in other ways.

Holt CA Course 1

7-6 Populations and Samples

About 39% of all U.S. households have houseplants. Lee surveys a random sample of households from two towns in his state. Compare the samples with the national percent.

Additional Example 2: Comparing Samples

For each sample, find the percent of the households that have houseplants.

Houseplant Ownership

Sample With Plants Without Plants

Town A 40 60

Town B 60 40

Holt CA Course 1

7-6 Populations and Samples

About 39% of all U.S. households have houseplants. Lee surveys a random sample of households from two towns in his state. Compare the samples with the national percent.

Additional Example 2 Continued

= 0.40 = 40%

Town A: = =# of households with plants total number of households

t 40 t 40 +

60

t40t 100

Town B: = =# of households with plants total number of households

t 60 t 60 +

40

t60t 100 = 0.60 = 60%

The percent of households with houseplants in Town A (40%) is close to the national percent. The percent of households in Town B (60%) is greater than the national percent.

Holt CA Course 1

7-6 Populations and Samples

About 22% of all U.S. households have pet fish. Rylan surveys a random sample of households from two towns in his state. Compare the samples with the national percent.

Check It Out! Example 2

For each sample, find the percent of the households that have pet fish.

Pet Fish Ownership

Sample With Pet Fish Without Pet Fish

Town A 25 75

Town B 55 45

Holt CA Course 1

7-6 Populations and SamplesCheck It Out! Example 2 Continued

= 0.25 = 25%

Town A: = =# of households with pet fish total number of households

t 25 t 25 +

75

t25t 100

Town B: = =# of households with pet fish total number of households

t 55 t 55 +

45

t55t 100 = 0.55 = 55%

The percent of households with pet fish in Town A (25%) is close to the national percent. The percent of households in Town B (55%) is greater than the national percent.

About 22% of all U.S. households have pet fish. Rylan surveys a random sample of households from two towns in his state. Compare the samples with the national percent.

Holt CA Course 1

7-6 Populations and Samples

A Web site consists of 400 pages. A Web designer estimates that 60 of the Web pages have broken links. In a random sample of 20 pages, 7 of the pages have broken links. Determine whether the manager’s estimate is likely to be accurate. Explain.

Additional Example 3: Evaluating Claims Based on Statistical Data

Set up a proportion to predict the total number of broken links.

broken links in sample pages sampled

total # of broken links # of web site pages

=

Holt CA Course 1

7-6 Populations and SamplesAdditional Example 3 Continued

Let x represent the number of actual links broken.

7 20

x 400

=

7 • 400 = 20 • x The cross products are equal.

2800 = 20x Multiply.

2800 20

20x 20

= Divide each side by 20.

140 = xThe estimate is not accurate because based on the sample, the number of pages with broken links is likely to be about 140.

Holt CA Course 1

7-6 Populations and Samples

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. Explain.

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

=

Holt CA Course 1

7-6 Populations and SamplesCheck It Out! Example 3 Continued

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

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

9600 = 40x Multiply.

9600 40

40x 40

= Divide each side by 40.

240 = x

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

8 40

x 1200

=