I feel like this all feels too easy when you're practicing but when you give the actual test ,the score is always underwhelming

but this is because you didn't studied or because the exercises are too lower level compared to the questions of the test?

It seems SAT Math is easy than our A levels

Yes, honestly, I'm studying for my Nigerian JAMB exams and SAT math is by far easier and less broad than JAMB or even my school A Level Math.

Will we be always given the margin of error on the SAT or will we ever have to calculate it?

I always see your comments on the videos/articles. Have you finished the DSAT math and/or reading course? If so, has it helped you improve your score?

I have decent understanding about the basics regarding the DSAT. Is collegeboard enough to prepare, and the bluebook practice tests?

Im not sure if it will be enough or not.But the more u practice the more u will be able to answers questions correctly.There are SAT questions bank on college board and u can also select question difficulty there .u can practice them to do better on SAT

What is this sign? ±

It means Plus or Minus. 2±1 could equal both 2+1=3 and 2-1=1

where do i find video about probability

On youtube there is a playlist which consicy of +40 videos about basics of probability,all these videos were filmed by Khan Academy and the voice actor there is Sal.

Main content

Course: Digital SAT Math > Unit 11

Lesson 9: Data inferences: advanced

Data inferences | Lesson

Google Classroom

A guide to data inferences on the digital SAT

What are data inferences questions?

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 those 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

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.

estimate = sample proportion \cdot population

Let's look at some examples!

A representative sample of households in City A reveals that

14.8 %

of the households in the sample have exactly two children under the age of

18

. If City A has a total of

59,317

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!

try: use sample data to make a prediction

An inspector examined a random sample of

500

bars of dark chocolate at the Nomnom Chocolate Factory and found

2

of the bars to be defective. The factory produces

60,000

bars of dark chocolate a week.

Write the sample proportion of the number of defective bars to the total number of bars as a fraction:

At this rate, how many defective dark chocolate bars is the Nomnom Chocolate Factory expected to produce in a week?

What is margin of error?

While we can make reasonable estimates using sample proportions, we can never be

100 %

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.

range = estimate \pm margin of error

For example, if a poll estimates that a political candidate will win

51 %

of the popular vote with a margin of error of

2 %

, what it actually means is that the poll is reasonably sure that the candidate will actually win

51 % \pm 2 %

of the popular vote, or anywhere between

49 %

and

53 %

Note: in the above example, there's still no

100 %

certainty that the candidate will win between

49 %

53 %

of the popular vote! However, the poll can be more confident in the

51 % \pm 2 %

estimate than in the exact

51 %

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!

try: use margin of error to draw a conclusion

A researcher surveyed a random sample of students from a large university about how often they talk to their parents. Using the sample data, the researcher estimated that

12 %

of the students in the population talk to their parents at least once per day. The margin of error for this estimation is

3 %

The researcher is reasonably confident that between

of the students at the university talk to their parents at least once per day.

If the researcher doubled the size of the random sample, the margin of error would likely

Your turn!

Practice: use sample rate to make a prediction

In a recent survey of

600

randomly selected registered voters in the town of Carrington,

482

are in favor of increasing funding for the town's mental health services. Based on the survey results, approximately how many of Carrington's

19,310

registered voters are in favor of increasing funding for the town's mental health services?

Practice: draw conclusion based on margin of error

Anya surveyed a random sample of members of a large gym about how often they visit the gym. Using the sample data, she estimated that

74 %

of gym members go to the gym at least once a week, with a margin of error of

3 %

. Which of the following is the most appropriate conclusion about all members of the gym, based on the given estimate and margin of error?

(Choice A)
Anya is $71 %$ ‍ to $77 %$ ‍ sure that less than half of the gym members go to the gym at least once a week.
(Choice B)
It is likely that the percentage of gym members who go to the gym at least once a week is between $71 %$ ‍ and $77 %$ ‍.
(Choice C)
At least $71 %$ ‍, but no more than $74 %$ ‍, of the gym members go to the gym at least once a week.
(Choice D)
It is unlikely that more than $74 %$ ‍ of the gym members go to the gym at least once a week.

Things to remember

\begin{aligned} estimate = sample proportion \cdot population \\ range = estimate \pm margin of error \end{aligned}

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

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aarohan567
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I feel like this all feels too easy when you're practicing but when you give the actual test ,the score is always underwhelming
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- juli
  Posted a year ago. Direct link to juli's post “but this is because you d...”
  but this is because you didn't studied or because the exercises are too lower level compared to the questions of the test?
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Saidbek Normaxmatov
Posted a year ago. Direct link to Saidbek Normaxmatov's post “It seems SAT Math is easy...”
It seems SAT Math is easy than our A levels
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- nwasorjustina
  Posted 3 months ago. Direct link to nwasorjustina's post “Yes, honestly, I'm studyi...”
  Yes, honestly, I'm studying for my Nigerian JAMB exams and SAT math is by far easier and less broad than JAMB or even my school A Level Math.
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Will we be always given the margin of error on the SAT or will we ever have to calculate it?
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  Posted 8 months ago. Direct link to munachisoonyilofor's post “I always see your comment...”
  I always see your comments on the videos/articles. Have you finished the DSAT math and/or reading course? If so, has it helped you improve your score?
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I finished this lesson in 14±2 minutes
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What is this sign? ±
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- Ian Altenhof
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  It means Plus or Minus. 2±1 could equal both 2+1=3 and 2-1=1
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zymalimtiaz16
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how to calculate the margin of error if asked in the test?
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Mohamad_Diab
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where do i find video about probability
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- CthulhuWakeUp
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  On youtube there is a playlist which consicy of +40 videos about basics of probability,all these videos were filmed by Khan Academy and the voice actor there is Sal.
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Ezra
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The best part of this section is getting the answer by simple multiplication, subtraction, and addition. You could do it in your mind lol.
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Dt.lxe
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For those who solved practice test 2 (digital), did you find it easier or harder than practice test 1?
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agastyapoduval
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I have decent understanding about the basics regarding the DSAT. Is collegeboard enough to prepare, and the bluebook practice tests?
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- Faiaz
  Posted 5 months ago. Direct link to Faiaz's post “Im not sure if it will be...”
  Im not sure if it will be enough or not.But the more u practice the more u will be able to answers questions correctly.There are SAT questions bank on college board and u can also select question difficulty there .u can practice them to do better on SAT
  Button navigates to signup page
  (2 votes)