Could we use a random sample to discover whether or not peoples’ education level

impacts their likelihood to vote in a presidential election?

In this lesson you will learn how to make inferences about a population with an unknown characteristic by analyzing

random samples.

Let’s Review

Representative sample

Valid inference

Random sampling method

A Common MistakeBlue is the preferred

color.Some students make an inference or generalization even if the data

doesn’t show a significant pattern.

Core Lesson

?

Trout

Walleye

Whitefish? ?

?

Unknown characteristic

Core Lesson

? ?

?

Random sample: 300 fish

45 Walleye

130 Whitefish

125 TroutInferences about

population

Core Lesson

More/less than

Twice as many as

Tends to increase/decrease

Making inferences

Core Lesson

45 Walleye

130 Whitefish

125 Trout

Random SampleThere are more trout and whitefish than walleye in the lake

There are about 1/3 as many walleye as trout

or whitefish

Whitefish is the most common fish

Inferences

In this lesson you have learned how to make inferences about a population with an unknown

characteristic by analyzing random samples.

Guided Practice

What inferences can be made from the graph?

Data: Survey of a random sample of Americans

Less than high school

High school degree

Some college College degree Graduate degree0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

40%

70%75%

84% 86%

% Voted

Extension Activities

Which is the most valid inference?A) Black is the least preferred color.B) More students prefer blue than prefer black and green combined.

C) Blue and green are the preferred colors.D) Pink is preferred to black.

Black Yellow Green Pink Blue TOTAL

74 105 215 79 227 700

Extension Activities

TOTAL

Create a survey question and five possible responses. Collect data from a sample of your class in a table like the one below. Make two inferences about your entire grade by analyzing the data from your sample.

Extension Activities

Explain why Kyle’s inference may be invalid.

Kyle: People with graduate degrees vote more often than people with only college degrees.

Less than high school

High school degree

Some college College degree

Graduate degree

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

40%

70%75%

84% 86%

% Voted

Quick Quiz

To predict middle school students’ ice cream preferences, a random sample of 1,300 students was surveyed about their preferences between ice cream flavors.

Chocolate Vanilla Mint Chocolate

Chip

Strawberry Cookie Dough

TOTAL

194 210 350 190 356 1300

1) Make two inferences about the population.

Quick Quiz

2) Which is the most valid inference from this sample data?a) Strawberry is the least preferred flavor.b) More students prefer cookie dough ice cream than prefer chocolate and vanilla combined.c) Cookie dough and mint chocolate chip arethe preferred ice cream flavors.d) Chocolate ice cream is preferred to strawberry