Final answer:
The student council's use of systematic sampling by selecting every 20th student may be valid if the list does not introduce bias, but mixed methods like simple random sampling or stratified sampling could lead to more accurate results.
Step-by-step explanation:
The student council at Eleanor Roosevelt High School wants to survey student opinions on the year's homecoming theme. They plan to use a systematic sampling method by selecting every 20th student from an alphabetized list. The validity of the survey results depends on how well this method represents the entire student population.
Systematic sampling can be effective if the list does not have a pattern that could introduce bias. However, if the list has a hidden periodicity that correlates with the homecoming theme preferences, it might lead to over- or under-representation of certain groups.
For greater validity, a mix of different sampling techniques such as simple random sampling, where each student has an equal chance of being selected, or stratified sampling, which ensures representation from all groups (like grade levels or demographics), could potentially produce more accurate results. Examples of different sampling methods include selecting 25 students randomly from each class year, using a random number generator to pick students, or ensuring that the sample matches the demographic proportions of the overall student body.