Which sampling method is being used?

Answer: Simple random sample Every group of 60 students has an equal chance of being selected because the principal randomly draws 60 distinct numbers from the full roster. This is the defining property of a simple random sample.

Which sampling method is being used?

Answer: Systematic sample Selecting every kth element after a random start is a systematic sample. It is not an SRS because not all possible groups of bolts have equal probability of being chosen.

Which sampling method is being used?

Answer: Cluster sample Classrooms (clusters) are randomly selected, and every student within the chosen clusters is surveyed. This is a cluster sample, distinguished from stratified sampling by sampling whole groups rather than within groups.

AP Statistics · Topic 3.3

Random Sampling and Data Collection Practice

Part of Collecting Data.(DAT-2.B)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$A high school principal wants to estimate the average number of hours per week that students spend on homework. She obtains a list of all 1,200 students from the registrar, assigns each student a number from 1 to 1,200, and uses a random number generator to select 60 distinct numbers. The students corresponding to those numbers are surveyed about their weekly homework hours.$
$Which sampling method is being used?$
- A
  $Cluster sample$
- B
  $Stratified random sample$
- C
  $Simple random sample$
  check_circle
- D
  $Systematic sample$
Why
$Every group of 60 students has an equal chance of being selected because the principal randomly draws 60 distinct numbers from the full roster. This is the defining property of a simple random sample.$
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Sample 2difficulty 1/5
$A factory wants to estimate the proportion of defective bolts produced in a day. Bolts come off the assembly line one at a time. The quality engineer randomly selects a starting position between 1 and 50 and then inspects every 50th bolt thereafter throughout the shift.$
$Which sampling method is being used?$
- A
  $Cluster sample$
- B
  $Systematic sample$
  check_circle
- C
  $Convenience sample$
- D
  $Simple random sample$
Why
$Selecting every kth element after a random start is a systematic sample. It is not an SRS because not all possible groups of bolts have equal probability of being chosen.$
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Sample 3difficulty 1/5
$A school district has 80 elementary school classrooms, each containing about 25 students. Researchers want to estimate the proportion of students who eat breakfast at home. They randomly select 8 of the 80 classrooms and survey every student in those chosen classrooms.$
$Which sampling method is being used?$
- A
  $Cluster sample$
  check_circle
- B
  $Systematic sample$
- C
  $Simple random sample$
- D
  $Stratified random sample$
Why
$Classrooms (clusters) are randomly selected, and every student within the chosen clusters is surveyed. This is a cluster sample, distinguished from stratified sampling by sampling whole groups rather than within groups.$
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Sample 4difficulty 1/5
$A teacher places all 28 of her students' names in a hat, mixes them, and draws 5 without replacement to form a focus group on classroom climate.$
$What sampling method is this?$
- A
  $Cluster sample$
- B
  $Simple random sample$
  check_circle
- C
  $Stratified sample$
- D
  $Convenience sample$
Why
$Drawing names from a thoroughly mixed hat without replacement gives every group of 5 students an equal chance of selection, the definition of an SRS.$
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Sample 5difficulty 1/5
$The "population" in a survey is$
- A
  $The group from which the sample is taken; the target group$
  check_circle
- B
  $100% always$
- C
  $Only the people surveyed$
- D
  $The sample itself$
Why
$Population = entire group of interest; sample = subset actually studied.$
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