Practice Random Sampling in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Random sampling is a method of selecting individuals from a population where every member has an equal chance of being chosen, ensuring the sample is unbiased and representative of the whole population.
Drawing names from a hat where all names are equally likely to be picked. No favoritism, no convenience, just pure chance. This is how we ensure the sample represents the whole population, not just the easy-to-reach people.
Showing a random 20 of 50 problems.
Example 1
challengeDesign a sampling plan to estimate average monthly grocery spending in a city with socio-economic strata of sizes , , , . You can afford surveys. Use proportional allocation.
Example 2
mediumA pollster correctly draws a simple random sample of 1000 voters but 600 refuse to answer. Does the final responding group remain a random sample, and what threat appears?
Example 3
hardTwo designs to study customer satisfaction at a chain with stores: (A) randomly pick stores and survey all customers; (B) randomly pick customers from a master list. Which is cluster sampling, and which is simple random?
Example 4
mediumWhen you draw a simple random sample of size without replacement from individuals, what is the probability any one named individual ends up in the sample?
Example 5
mediumA school has 600 students in three grades (200 each). A researcher wants 60 students and uses a random number generator to pick 60 from all 600 IDs. Each grade ends up with a different count. Is this still a valid random sample?
Example 6
challengeA researcher claims a 'random sample' was obtained by posting an online form on social media. Identify two distinct biases in this method.
Example 7
mediumA manager wants a random sample of 5 from 200 employees but only has a list of the day-shift (120 of them). She randomly picks 5 from that list. What is wrong, and what is the actual population sampled?
Example 8
easyA researcher numbers 50 patients and uses a random draw to pick 10. One picked patient is unavailable, so she just picks the next person on her ward instead. Did she preserve random sampling?
Example 9
mediumA pollster claims a 'random sample' was obtained by surveying every visitor to a website who clicked a banner ad. Identify the type of sampling and one reason it is not random.
Example 10
easyWhy is random sampling preferred over convenience sampling when estimating a population mean?
Example 11
easyA researcher wants to study high-school students. He stands outside one school during lunch and surveys whoever stops. What is wrong with calling this a random sample of high-school students?
Example 12
challengePollster A samples 100% of one small neighborhood; Pollster B takes a true random sample of 500 from the whole city of 200,000. To estimate citywide opinion, which design is sounder, and what statistical idea explains why a smaller random sample beats a large convenience census of one area?
Example 13
hardA university has 12,000 students: 7,200 undergraduates and 4,800 postgraduates. A researcher wants a stratified sample of 200 students. (a) How many undergraduates and postgraduates should be in the sample? (b) How does this compare to what might happen with a simple random sample?
Example 14
easyA mall surveys every th shopper who walks through the main entrance. What sampling method is this?
Example 15
easyA school has 500 students numbered 001–500. Describe how to select a simple random sample of 20 students using a random number generator.
Example 16
challengeA researcher wants each of 1000 customers to have the same selection chance but wants exactly 100 selected. She assigns each a uniform random number in [0,1] and takes the 100 smallest. Does every customer have an equal chance of being in the sample? Justify.
Example 17
mediumA teacher wants a random sample of 6 from 24 students. He shuffles a deck mapping 24 cards to students and deals 6. A student asks: does shuffling once give each student an equal chance? Justify.
Example 18
hardA poll randomly picks people from a city's voter registration list to estimate support for a referendum among 'all city residents.' What population is the sample technically representative of, and why might it differ from 'all residents'?
Example 19
easyName the type of sampling where the population is divided into groups and a random sample is taken from each group.
Example 20
mediumA researcher uses random sampling to estimate average household income in a city of 50,000 homes, sampling 500. A colleague says 'random sampling guarantees the sample mean equals the population mean.' Is the colleague right?