MATHEMATICS · Multi-part · AP · AP Statistics · Collecting Data · Collecting Data
Problem
Each sampling method suffers from a form of bias. Identify the bias, tell how the sample statistic might differ significantly from the population parameter, and suggest how the problem might be corrected.
(1) To gather feedback on his teaching, Professor Jones invites his students to visit his website and respond to a brief questionnaire. He is depressed to discover that 68% of those who respond are dissatisfied with his teaching.
(2) To assess consumer response to its new cereal flavor, a cereal company passes out free samples at a local mall and offers shoppers a $5.00 gift certificate if they fill out a brief form evaluating the new product. They find that 94% of respondents like the new flavor.
(3) The dining committee of the student council surveys students in the lunch hall, asking them, "Do you prefer eating in the lunch hall to eating off campus or bringing your own lunch?" They are mildly surprised to learn that 93% of the students surveyed prefer the dining hall.
(4) A group seeking taxpayer support for a new playground sends pollsters to all local PTA meetings to ask, "Do you support the use of city taxes to fund a new park that will provide a safe and convenient recreation facility for your children?" A gratifying 88% respond yes.
(5) After getting a ticket for running a stop sign, a statistics professor polls a random sample of citizens to ask, "Should the government be allowed to limit the freedom of private citizens to utilize our neighborhood roads as we deem necessary?" He tells the judge at his hearing that 97% of the citizens polled are against stop signs.
(6) For twenty years, Mrs. Bohackett has kept a daily log of birds sighted at her backyard feeder. Over the last ten years, the first appearance of a white-throated sparrow in spring has steadily moved earlier in the year by thirteen days. She attributes the change to global warming.