Systematic approaches for selecting a subset of individuals from a population. The main probability methods are: simple random sample (SRS), stratified random sample, cluster sample, and systematic sample. Convenience sampling is a non-probability method that is generally biased.
You want to know the average GPA of 10,000 students. You can't ask everyone, so you pick a sample. How you pick matters enormously: grab the first 50 students you see in the cafeteria (convenience—biased), or give every student a number and use a random number generator to pick 50 (SRS—unbiased). Stratified sampling is like making sure you get proportional numbers from each grade level. Cluster sampling picks entire groups (like randomly selecting 5 classrooms and surveying everyone in them).
Showing a random 20 of 50 problems.
Example 1
medium
A researcher splits a city into neighborhoods, randomly picks a few neighborhoods, and surveys everyone there. Stratified or cluster?
Example 2
easy
What does SRS stand for?
Example 3
easy
Fill in the blank: a ____ sample is one in which subgroups are deliberately sampled separately.
Example 4
medium
Describe four sampling methods: simple random, stratified, cluster, and systematic. Compare their advantages and disadvantages.
Example 5
medium
A factory inspects every 50th item. If a malfunction makes every 50th item defective, what problem arises?
Example 6
medium
What is undercoverage bias?
Example 7
hard
A researcher randomly selects every 10th name from an alphabetical list of 1000 employees. Explain why this is systematic sampling, calculate the starting point needed, and describe a potential bias if the list is alphabetized by department.
Example 8
easy
A study randomly chooses 4 of 50 high schools and surveys ALL students in each. Method?
Example 9
easy
A pollster surveys 50 friends in their dorm. Method? Likely biased?
Example 10
easy
You divide students into grade levels, then randomly sample within each grade. Which method is this?
Example 11
medium
To estimate average household income, which method best ensures both rich and poor neighborhoods are represented?
Example 12
medium
A teacher pulls names from a hat to pick 5 of 30 students. Method?
Example 13
hard
What is multistage sampling?
Example 14
medium
A school has 1000 students: 60% female, 40% male. A stratified sample of 50 by sex should contain how many of each?
Example 15
medium
True or false: a larger SRS is always more accurate than a smaller one of the same population.
Example 16
medium
A teacher wants an SRS of 4 from 20 students using a random number table. Describe the key property the result must have.
Example 17
challenge
The 1936 Literary Digest poll predicted Landon would beat Roosevelt based on 2.4 million respondents. Roosevelt won in a landslide. Identify the TWO main sampling errors.
Example 18
challenge
Explain the core difference between stratified and cluster sampling using how each handles the subgroups it forms.
Example 19
easy
You randomly pick 5 entire classrooms and survey everyone in them. Which method is this?
Example 20
hard
A school has classes of widely varying sizes. Why might cluster sampling of classes give estimates of student attitudes that are biased toward larger classes if you don't reweight?