To determine the favorite music genre of students in a school, the principal surveys only the students in the school band. Why might an inference from this sample be invalid?

The sample is not random and is likely biased.

The principal should have surveyed teachers instead.

A researcher takes three separate random samples of 100 voters each to predict an election. The results show 54%, 57%, and 55% support for a candidate. What is the most reasonable conclusion?

The election is too close to call.

The samples are not representative.

The candidate's support is likely between 54% and 57%.

The candidate will lose the election.

A survey of 20 members of a town's gardening club shows 18 of them use brand X fertilizer. Which conclusion is an invalid inference?

90% of the gardening club members surveyed use brand X.

Most people in the gardening club likely use brand X.

About 90% of all people in the town use brand X.

The sample is biased if used to represent the whole town.

Making Inferences from Data Practice — Grade 7 math

Lesson 2: Making Inferences from Data — Practice Questions

1. A random survey of 80 students at a middle school found that 48 of them have a pet. Based on this sample, it can be inferred that ___% of the students at the school have a pet.
2. To determine the favorite music genre of students in a school, the principal surveys only the students in the school band. Why might an inference from this sample be invalid?
- A. The sample size is too large.
- B. The sample is not random and is likely biased.
- C. The question is too personal.
- D. The principal should have surveyed teachers instead.
3. A company manufactures 10,000 smartphones. A random sample of 500 phones finds that 15 have a defective screen. Based on this, you can infer that about ___ phones in the entire batch are defective.
4. A researcher takes three separate random samples of 100 voters each to predict an election. The results show 54%, 57%, and 55% support for a candidate. What is the most reasonable conclusion?
- A. The election is too close to call.
- B. The samples are not representative.
- C. The candidate's support is likely between 54% and 57%.
- D. The candidate will lose the election.
5. A survey of 20 members of a town's gardening club shows 18 of them use brand X fertilizer. Which conclusion is an invalid inference?
- A. 90% of the gardening club members surveyed use brand X.
- B. Most people in the gardening club likely use brand X.
- C. About 90% of all people in the town use brand X.
- D. The sample is biased if used to represent the whole town.
6. A random sample of 40 students from a large university has a mean GPA of 3.1. What is the most reasonable inference about the mean GPA of all students at the university?
- A. The mean GPA of all students is exactly 3.1.
- B. The mean GPA of all students is about 3.1.
- C. Every student at the university has a GPA of 3.1.
- D. The mean GPA of all students is higher than 3.1.
7. A quality check of 300 randomly selected T-shirts found that 9 had a printing error. Based on this sample, it is reasonable to infer that about ___% of all T-shirts have a printing error.
8. The mean time a random sample of 25 customers spent in a store was 18 minutes. A valid inference is that the mean time all customers spend in the store is about ___ minutes.
9. A biologist catches and releases 150 fish from a lake. He finds that 12 of them have a particular tag. A reasonable inference is that around ___% of all fish in the lake have that tag.
10. In a random sample of 80 households in a town, 20 owned a cat. Which statement is the most appropriate conclusion to draw from this sample?
- A. Exactly 25% of all households in the town own a cat.
- B. It is likely that around 25% of all households in the town own a cat.
- C. Every fourth household in the town owns a cat.
- D. No more than 20 households in the town own a cat.