Unit 3: Collecting Data (Sampling Methods) Teacher Answer Key — Page 1 of 2
KEY
AP Statistics Standard Solution Set
A luxury resort wants to assess guest satisfaction with premium amenities. They randomly select 40 guests from penthouse suites, 80 guests from ocean-view rooms, and 120 guests from standard garden rooms.
Method Stratified Random
Bias & Explanation
Guarantees proportional room category feedback. High-paying suite guests may exhibit nonresponse bias, overrepresenting standard guests.
To estimate the average squirrel population in a massive state park, wildlife biologists divide the park into 120 equal grid sectors. They randomly select 10 sectors and count every single squirrel found within those 10 sectors.
Method Cluster Sampling
Bias & Explanation
Potential geographic cluster bias. If selected grids happen to hit major water sources or food-dense areas, population density will be overestimated.
A fitness influencer with 1 million followers posts a poll on their Instagram story asking: "How many days a week do you exercise?" Over 15,000 followers submit their votes.
Method Voluntary Response
Bias & Explanation
Severe voluntary response bias. Fitness followers are highly self-selected and active, which severely overestimates general population exercise habits.
A stadium security director wants to inspect bags for prohibited items. They decide to search the belongings of every 12th fan who passes through the main entrance gates.
Method Systematic Sampling
Bias & Explanation
Very unbiased. Spreads samples evenly across entry flows. However, if groups enter sequentially, only one group representative might be chosen.
A local library wants to know if residents support a new technology levy. A coordinator randomly draws 150 library card numbers from their database of 5,000 active cardholders to contact.
Method Simple Random (SRS)
Bias & Explanation
Severe undercoverage bias. Cardholders represent library supporters, systematically overestimating levy approval compared to general tax-payers.
Concept Check Grading Guidelines (2 pts)
Explain why increasing the sample size of a naturally biased sampling method (such as voluntary response or convenience sampling) does not reduce the bias of the overall results.
Exemplary Teacher Solution:
Bias is a systematic error resulting from the sampling method itself, not a random chance variation. If a method inherently over-selects or under-selects specific groups (e.g., fitness followers in an Instagram poll), collecting a larger sample simply increases the size of the biased pool. It increases precision (decreases variability) but centers that precise estimate around a systematically incorrect, biased value.
Unit 3: Collecting Data (Sampling Methods) Teacher Answer Key — Page 2 of 2
