Testinar Grade 7 math

Populations and Samples

Students will build Grade 7 mastery of populations and samples using models, equations, and test-style reasoning.

CH08-01 Statistics
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. A principal wants to know the average number of hours students study per week at her school. Which is the BEST way to collect a representative sample?

    1. Survey only the students in her own homeroom
    2. Survey the first \(30\) students who arrive Monday morning
    3. Randomly select \(30\) students from each grade
    4. Survey only students on the honor roll

  2. A school wants to know which sports are most popular among its students. Compare these two methods: Why is Method 2 more likely to produce an accurate estimate?

    1. Method 1: Ask the students in the first period gym class
    2. Method 2: Randomly select 30 students from a complete list of all students

  3. A clothing store manager wants to find out which style of jeans is most popular among teenagers in her city. If she only surveys customers who shop at her store on Saturday afternoons, what type of bias is present?

    1. Convenience sampling
    2. Voluntary response bias
    3. Leading question bias
    4. Non-response bias

  4. A survey asks: "Don't you agree that our school lunch program provides terrible food?" What sampling problem does this question have?

    1. Convenience sample
    2. Leading question
    3. Voluntary response bias
    4. Insufficient sample size

  5. Which group is an example of a population in a statistical study?

    1. \(200\) students randomly selected from all high schools in Texas
    2. All teenagers who own a smartphone
    3. Shoppers interviewed at one mall on Saturday
    4. The \(50\) customers called to participate in a phone survey

  6. A museum director wants to estimate how many visitors will spend more than one hour at the museum. She collects data by asking every \(10\)th visitor who enters. Is this a good sampling method?

    1. No; it is a convenience sample
    2. No; it uses voluntary response bias
    3. Yes; it is a systematic random sample
    4. Yes; it is a stratified sample

  7. A school wants to estimate the average amount of time students spend on homework per night. Which sample size is best?

    1. \(10\) students
    2. \(25\) students
    3. \(100\) students
    4. \(1000\) students

  8. A company wants to estimate the average salary of all its employees. It randomly selects \(50\) employees and calculates the mean. The \(50\) employees are a \underline{\hspace{3cm}} of all company employees.

    1. population
    2. sample
    3. statistic
    4. parameter
Teacher and parent reference

Answer key and explanations

  1. C. Randomly select \(30\) students from each grade

    This is stratified random sampling: dividing the population into groups (grades) and randomly selecting from each ensures all grade levels are represented proportionally. This avoids bias toward any one grade's study habits.

  2. B. Method 2: Randomly select 30 students from a complete list of all students

    Random selection from all students ensures the sample is representative because it includes diverse students: athletes and non-athletes, different grade levels, and different interests. Method 1 only surveys gym class students, who are more likely to favor sports, making that sample biased and unrepresentative of all students.

  3. A. Convenience sampling

    Surveying only customers at one store at one time is a convenience sample because it only includes people who are easy to reach, not a random selection of all teenagers in the city.

  4. B. Leading question

    The question is phrased to suggest a particular answer ("terrible food") rather than remaining neutral, which influences how people respond.

  5. B. All teenagers who own a smartphone

    A population is the entire group of interest. All teenagers who own a smartphone is the complete group; the other options describe samples or parts of a larger population.

  6. C. Yes; it is a systematic random sample

    Asking every \(10\)th visitor is systematic random sampling. Since the pattern (every 10th) doesn't depend on characteristics of individual visitors, it provides a representative, unbiased sample of all museum visitors.

  7. C. \(100\) students

    A sample of \(100\) students balances accuracy with practicality. Samples of \(10\) and \(25\) are too small to reliably represent the whole school; \(1000\) would give similar accuracy but be costly and time-consuming to conduct.

  8. B. sample

    A sample is a subset of the population selected for study. The \(50\) employees are part of the entire employee population, so they form the sample.

Free Testinar sample Reviewed November 6, 2026 testinar.com
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