7th Grade Random Sampling and Inference Test with Point Values (PDF)

7th Grade math test: Random Sampling and Inference – Maths PDF

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This random sampling test for 7th Grade covers random sampling and inference (Common Core 7.SP.A.1, 7.SP.A.2), with a free PDF to print.

This 45-minute test checks populations and samples, representative and biased samples, random sampling, and using samples to estimate a population (Common Core 7.SP.A.1-2). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Random Sampling and Inference
Standards: 7.SP.A.1, 7.SP.A.2
Time: 45 minutes
Total: 20 points

Random sampling test: questions

Question 1 – Population and sample [2 pts]

A voter survey.

A city surveys 30 of its 500 voters. Name the population and the sample, and tell what the survey is meant to find out.

Question 2 – Choose the sample [2 pts]

Three ways to survey about favorite music.

The city wants to know the favorite kind of music of all residents. Which method is most likely to be representative? Explain why one of the others is biased.

Question 3 – Estimate the population [2 pts]

In a random sample of 70 students, 21 ride the bus. Estimate how many of the 1,500 students in the school ride the bus.

Question 4 – Variability [2 pts]

Eleven samples of 50 students.

Each dot is the percent who walk to school in a random sample of 50 students. Find the median percent. Estimate how many of 2,000 students walk.

Question 5 – Random method [2 pts]

Describe a method for choosing a random sample of 25 students from a class of 150 students. Explain why it is random.

Question 6 – Tag and recapture [2 pts]

A park ranger tags 40 deer and releases them. Later a random sample of 30 deer includes 6 tagged deer. Estimate the number of deer in the park.

Question 7 – Compare predictions [2 pts]

Aisha predicts 40% of a population like green apples from a sample of 10. Noah predicts 30% from a sample of 110 that had 33 who like green apples. Whose prediction is probably better, and why?

Question 8 – Three samples [3 pts]

Three samples about a new lunch menu.

Find the percent in each sample who like the new menu. (1 point)
Combine the three samples and find the overall percent. (1 point)
Use the combined percent to estimate how many of 800 students like the menu. (1 point)

Question 9 – Sampling variability [3 pts]

Twelve random samples of 100 voters.

Find the median percent. (1 point)
Find the range of the sample percents. (1 point)
Estimate the number of yes votes among 20,000 voters, and explain why the estimate is not exact. (1 point)

Key facts behind this random sampling test

Key facts

A population is the whole group; a sample is a part of it.
A random sample gives every member an equal chance of being chosen.
Biased samples over-represent some members and give poor estimates.
Estimate a population count by multiplying the sample proportion by the population size.
Larger random samples vary less and give better estimates.

How to use this random sampling test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

Voter.. post

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