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7.123 Using samples to make inferences Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 7 Math worksheet provides structured practice on 7.123 Using samples to make inferences. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

7.123 Using samples to make inferences - In multiple-choice items, students select the inference that is supported by sample data and choose an appropriate statement about sampling error. (CCSS 7.SP.A.2; FL MA.7.DP.1.3; TX 7.12(B); VA 7.PS.2)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 7

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 7.123 Using samples to make inferences skill assessments:

Problem 1Difficulty: Mastery

A survey is trying to learn whether people wear a seatbelt every time they ride in a car in all residents in Ravenwood Park Town. The surveyor questioned 30 people by asking only members who were at the first meeting of the month. In that group, 15 said yes. Which statement is best? (Think about bias and sampling error.)

AYou can safely generalize to all residents in Ravenwood Park Town because any sample gives the same result as long as it has 30 people.

BThe only possible problem is sampling error, so repeating the survey with the same method will remove all problems.

CAbout 50.0% of all residents in Ravenwood Park Town wear a seatbelt every time they ride in a car. Because 30 people were asked, the result has no sampling error and is unbiased.

DThis result might not represent all residents in Ravenwood Park Town because the sample was not random and could be biased. Even with a large sample, bias can affect the inference, and sampling error does not fix that.

Solution & Explanation:Because the people were chosen in a specific way (only members who were at the first meeting of the month), the sample may not be representative of the whole population all residents in Ravenwood Park Town. That is bias. Sampling error is the natural random variation you get with random samples, but a biased method can lead to a misleading estimate even if you ask many people.

Problem 2Difficulty: Mastery

Five different random samples of size 80 were taken from all 7th graders at Cypress Hills Middle School to study whether people have ever volunteered in the community. The sample percents that said yes were: 30.0%, 31.2%, 27.5%, 25.0%, 25.0%. Which statement is the best inference about the population and sampling error?

ASampling error means all five sample percents must be added together to get the exact population percent.

BBecause the samples give different percents, you cannot make any inference about the population at all.

CThe population percent is probably near the middle of these results (around 27.7%). The differences among the sample percents are due to sampling error.

DThe population percent changes each time a sample is taken, so it must be exactly 25.0% now.

Solution & Explanation:Repeated random samples usually give slightly different results. That spread is sampling error. To infer the population percent, you look for a typical value near the center of the sample results (about 27.7%), not an exact value from one sample.

Problem 3Difficulty: Mastery

A coach wants to estimate whether people think the school should add more benches in hallways in all students at Hillcrest Creek Middle School. Random Sample 1: 42 out of 80 said yes (52.5%). Random Sample 2: 48 out of 80 said yes (60.0%). Which statement best explains these results and uses correct ideas about sampling error?

AOne of the samples must be wrong because a random sample always matches the population exactly.

BThe two sample percents are different, and that can happen because of sampling error. Both samples suggest the true population percent is somewhere around the middle of 52.5% and 60.0%, not exactly either one.

CThe population changed between the two samples for sure. Sampling error cannot cause different sample percents.

DThe true population percent is exactly 52.5% if Sample 1 was taken first.

Solution & Explanation:Even when you sample randomly, two different samples can give different results. That difference is sampling error (random variation). You use the sample(s) to estimate the population percent, but you do not assume either sample is exact.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 7 Math students. It aligns with educational standard 7.123 (Practice and review Grade 7 math skill 7.123: Using Samples to Make Inferences.).