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Simon Brainerd

Sampling

Study notes and exact practice on populations, samples, bias, random selection, reliability, survey flaws, and larger-scale sampling designs.

These sections are built to force recognition, discrimination, and setup. The questions are intentionally less subjective than a normal study guide. Most answers are short, exact, numerical, or classification-based.

Best use: try each question before opening the answer. Treat each section like a progression: identify the concept, sort the design, compute a simple quantity if needed, then explain why the method works or fails.

Progress

0 of 36 questions marked correct.

Populations, samples, and study targets

Learn what the study is actually trying to describe before doing anything else.

Core ideas

  • The population is the full group you want information about.
  • The sample is the subset you actually observe.
  • A study can only speak cleanly about the population if the sample was chosen in a defensible way.
  • Before analyzing numbers, identify who the target group is and who was actually measured.

What to lock in

  • Ask: “Who do we want to know about?” That is the population.
  • Ask: “Who gave the data?” That is the sample.
  • If those are badly misaligned, the study is already weak.
Question 1 — Count the sample

A school has 2,400 students. A survey collects responses from 180 students. Enter the sample size.

Sample size = 180.
Question 2 — Count the population

Using the same scenario, enter the population size.

Population size = 2,400.
Question 3 — Name the target group

A city wants to estimate the percentage of all households with internet access. It interviews 500 households. Type either population or sample: “all households in the city”.

Population.
Question 4 — Name the observed group

Same scenario. Type either population or sample: “the 500 households that were interviewed”.

Sample.
Question 5 — Sample fraction

If a population has 1,200 individuals and a sample contains 60, what percent of the population is in the sample? Enter only the number.

60 / 1200 = 0.05, so the sample is 5% of the population.
Question 6 — Core distinction

Type the single word that completes this statement: “The population is the full target group; the sample is the group actually ______.”

A correct completion is: observed. Measured, studied, or surveyed also capture the same idea.

Bias, convenience samples, and voluntary response

Learn to classify weak designs quickly and exactly.

Core ideas

  • A convenience sample is chosen because it is easy to reach.
  • A voluntary response sample is made of people who choose themselves.
  • Bias means the design systematically favors some outcomes or groups.
  • A large bad sample is still bad. Scale does not fix a broken design.

Fast classification rule

  • If the researcher grabs whoever is nearby, think convenience.
  • If people jump in because they want to, think voluntary response.
  • If either setup leaves some outcomes more likely than others, think bias.
Question 7 — Classify the design

A student stands outside the gym and surveys the first 40 people who walk out. Type one answer: convenience, voluntary, or random.

Convenience sample.
Question 8 — Classify the design

A radio station asks listeners to text in whether they support a tax increase. Type one answer: convenience, voluntary, or random.

Voluntary response sample.
Question 9 — Bias judgment

Type yes or no: Does a convenience sample often create bias?

Yes. Convenience sampling often favors certain groups and produces bias.
Question 10 — Strong opinions problem

Type the missing phrase: Voluntary response samples often overrepresent people with ______ ______.

Strong opinions.
Question 11 — Large sample trap

Type true or false: A sample of 20,000 volunteers is automatically better than a random sample of 1,000 people.

False. A huge biased sample can still be badly wrong.
Question 12 — Exact classification

A professor emails the whole class: “Reply if you think the exam was unfair.” Type one answer: convenience, voluntary, or simple random.

Voluntary response. Students choose themselves into the response group.

Simple random samples and random digits

Move from the concept of fairness to the mechanics of actual selection.

Core ideas

  • A simple random sample of size n gives every possible sample of size n the same chance to be selected.
  • Random choice blocks favoritism by the sampler and blocks self-selection by respondents.
  • Random digits and software are practical tools for carrying out this idea.
  • Labeling matters: if the population has 80 individuals, labels must cover 01 through 80.

Selection sequence

  • List the population.
  • Assign equal-length labels.
  • Read random digits in matching group lengths.
  • Skip impossible labels and repeated labels when sampling without replacement.
Question 13 — Label length

A population has 84 individuals. How many digits should each label have in a random-digit setup? Enter only the number.

2 digits. You would label them 01 through 84.
Question 14 — Valid label count

If the population is labeled 01 through 84, how many two-digit labels are invalid? Enter only the number.

There are 100 two-digit combinations from 00 to 99. Valid labels are 01 to 84, which is 84 labels. Invalid labels = 16.
Question 15 — Accept or reject

Population labels are 01 through 40. You read the random digit groups 07, 41, 18, 18, 03. If sampling without replacement, how many of these groups are accepted? Enter only the number.

Accepted: 07, 18, 03. Reject 41 because it is outside the population and reject the second 18 because it is a repeat. Total accepted = 3.
Question 16 — Equal chance statement

Type true or false: In a simple random sample, it is enough that each individual has some chance to be chosen; the possible samples do not need equal chance.

False. In a true SRS, every possible sample of the given size must have equal chance.
Question 17 — Number of labels

If a class roster has 250 students, what is the smallest equal label length that works for all students? Enter only the number of digits.

3 digits. You would label 001 through 250.
Question 18 — Main purpose of random choice

Type the missing word: Random choice attacks ______ by removing personal choice from sample selection.

Bias.

Inference, reliability, and sample size

Separate random variation from systematic bias, and learn what larger samples really buy you.

Core ideas

  • Inference means using the sample to say something about the population.
  • Random samples vary from sample to sample because of chance.
  • That variation is not meaningless noise; it follows probability laws.
  • Larger random samples usually reduce random error, but they do not erase bias.

Key learning distinction

  • Bias problem: wrong method.
  • Chance variation problem: even a good method produces slightly different results from sample to sample.
  • Larger n: better precision, not automatic truth.
Question 19 — Define inference

Type the one word that completes this: Using a sample to draw conclusions about a population is called statistical ______.

Inference.
Question 20 — Chance variation

Type yes or no: If two random samples are taken from the same population, should you expect exactly the same estimate every time?

No. Random samples differ because of chance variation.
Question 21 — Which issue is it?

A sample is chosen randomly, but the result differs slightly from another random sample. Type one answer: bias or chance.

Chance. Proper random sampling still produces sample-to-sample variation.
Question 22 — Which issue is it?

A survey uses only people who respond to a web banner ad. Type one answer: bias or chance.

Bias. The method itself systematically favors certain people.
Question 23 — Bigger sample logic

Type true or false: Increasing sample size usually reduces random error in a good random sample.

True. Larger random samples usually increase precision.
Question 24 — Bigger sample limitation

Type true or false: Increasing sample size always fixes bias.

False. A large biased sample can still be wrong in the same direction.

Stratified sampling and multistage sampling

Learn when a clean SRS is not the only serious design.

Core ideas

  • In a stratified design, you divide the population into strata first, then take separate random samples within each stratum.
  • In a multistage design, you sample in layers, often from large groups down to smaller ones.
  • Stratification often improves precision by ensuring relevant groups are represented.
  • Multistage designs are common when the population is large and geographically spread out.

Fast distinction

  • Stratified: divide by known group type, then sample inside every group.
  • Multistage: sample groups first, then sample within selected groups.
Question 25 — Identify the design

A state is divided into urban, suburban, and rural strata. Then an SRS is taken from each stratum. Type one answer: stratified or multistage.

Stratified.
Question 26 — Identify the design

A country randomly selects counties, then schools within those counties, then students within those schools. Type one answer: stratified or multistage.

Multistage.
Question 27 — Count the total sample

A stratified sample takes 20 people from each of 3 strata. What is the total sample size? Enter only the number.

20 × 3 = 60.
Question 28 — More represented groups

Type yes or no: One purpose of stratified sampling is to make sure important groups are represented in the final sample.

Yes.
Question 29 — Stages count

A design selects states, then counties, then neighborhoods, then households. How many stages are listed? Enter only the number.

4 stages.
Question 30 — Best label

Type the better design label for this sentence: “Sample groups first, then smaller groups within them.” Enter one answer: stratified or multistage.

Multistage.

Undercoverage, nonresponse, wording effects, and changing survey methods

See how a random design can still break once real human data collection begins.

Core ideas

  • Undercoverage happens when some groups are left out of the chance to be sampled.
  • Nonresponse happens when selected people cannot be reached or refuse to answer.
  • Response bias happens when answers are inaccurate because of pressure, wording, memory, or social effects.
  • Telephone and internet survey methods change over time because human communication habits change.

Classification cues

  • Missed from the frame: undercoverage.
  • Chosen but silent: nonresponse.
  • Answer distorted: response bias or wording effect.
  • Old contact method failing: technology shift.
Question 31 — Pick the flaw

A survey uses only landline phone numbers and misses households that use only cell phones. Enter one answer: undercoverage, nonresponse, or wording.

Undercoverage.
Question 32 — Pick the flaw

A random sample is selected correctly, but 35% of the people refuse to answer. Enter one answer: undercoverage, nonresponse, or wording.

Nonresponse.
Question 33 — Pick the flaw

A survey asks, “Do you support the sensible policy of reducing wasteful spending?” Enter one answer: undercoverage, nonresponse, or wording.

Wording effect. The phrasing pushes respondents toward one side.
Question 34 — Response rate calculation

A sample of 250 people is selected. Only 175 provide usable responses. What is the response rate as a percent? Enter only the number.

175 / 250 = 0.70, so the response rate is 70%.
Question 35 — Why phone methods changed

Type true or false: The spread of cell phones and call screening made older random-digit-dialing methods less straightforward.

True.
Question 36 — Final classification

Type the best one-word answer. If people are selected correctly but then many ignore the survey invitation, the main problem is ______.

Nonresponse.