Main content

## SAT

### Course: SAT > Unit 6

Lesson 5: Problem Solving and Data Analysis: lessons by skill- Ratios, rates, and proportions | Lesson
- Percents | Lesson
- Units | Lesson
- Table data | Lesson
- Scatterplots | Lesson
- Key features of graphs | Lesson
- Linear and exponential growth | Lesson
- Data inferences | Lesson
- Center, spread, and shape of distributions | Lesson
- Data collection and conclusions | Lesson

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# Data inferences | Lesson

## What are data inferences questions, and how frequently do they appear on the test?

When we want to answer questions like "how many voters feel positively about a new law" or "what percentage of Americans exercise regularly", it's often impractical to ask everyone—it would take a lot of time and effort to ask every voter, let alone every American!

Instead, when we have questions about a large

**population**, we often answer these questions by surveying a**representative sample**: a smaller set of people whose answers can give us a good idea of how the population would answer the same questions. In this lesson, we'll learn to:

- Make generalizations about a population based on sampling data
- Use margin of error to describe the uncertainty of sampling

On your official SAT, you'll likely see

**1 question**that tests your ability to make inferences based on sampling data.**You can learn anything. Let's do this!**

## How do I make generalizations about a population using sampling data?

### Estimating using sample proportions

A

**random sample**drawn from a population is representative of the population. With a representative sample, we can multiply the by the population to get an estimate.#### Let's look at some examples!

A representative sample of households in City A reveals that 14, point, 8, percent of the households in the sample have exactly two children under the age of 18. If City A has a total of 59, comma, 317 households, approximately how many of them have exactly two children under the age of 18 ?

50 seniors at a particular high school are randomly selected for a survey. 21 of them report riding their bikes to school at least once a week. If there are 300 seniors at this high school, what is a reasonable estimate of the total number of seniors who ride their bikes to school at least once a week?

### Try it!

## What is margin of error?

**Note:**questions about margin of error appear very rarely on the test. When they do appear, the margins of error are given—we don't need to calculate them ourselves.

While we can make reasonable estimates using sample proportions, we can never be 100, percent certain that the population proportion matches the sample proportion

*exactly*. Margins of error let us address the uncertainty inherent to sampling.The margin of error is most commonly given as a percentage. When given a percent estimate and a margin of error, we can establish a range around the estimate by adding and subtracting the margin of error.

For example, if a poll estimates that a political candidate will win 51, percent of the popular vote with a margin of error of 2, percent, what it actually means is that the poll is reasonably sure that the candidate will actually win 51, percent, plus minus, 2, percent of the popular vote, or anywhere between 49, percent and 53, percent.

**Note:**in the above example, there's still no 100, percent certainty that the candidate will win between 49, percent to 53, percent of the popular vote! However, the poll can be more confident in the 51, percent, plus minus, 2, percent estimate than in the exact 51, percent estimate.

The larger a sample size is, the smaller the margin of error will be. Think about it this way: if we want to make an estimate about a population of a million people, we'll get a more accurate result if we ask a random sample of 5000 people than if we ask only a random sample of 50.

### Try it!

## Your turn!

## Things to remember

The larger a sample size is, the smaller the margin of error will be.

## Want to join the conversation?

- Best of luck to anyone who's givin sat in the near future!(66 votes)
- Thank you, I needed that. Wish me luck!(3 votes)

- Sometimes I see questions that say "with a 95% confidence rate" or something. What does that mean and what topic does that come under?(7 votes)
- I was also confused by questions like that! I found this video (https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/introduction-confidence-intervals/v/interpreting-confidence-intervals-example) and it helped me understand what the confidence level/rate means. I hope this helps you too! Good luck!(8 votes)

- SAL KHAN! I love you. Your efforts help a lot(8 votes)
- I wanna know are these questions in calculator or no calculator part?(3 votes)