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For her statistics project, Freda wants to find the proportion of high school students who believe learning math is necessary, regardless of their future majors. She conducts a survey on her statistics classmates and finds that 82 percent of them believe it is necessary to learn math. Is Freda’s sample a random sample and good representation of the population in her study? If so, what can Freda conclude about the proportion of high school students who believe learning math is necessary? If not, propose a random sample which Freda should be conducting her survey

1 answer

Freda's sample of statistics classmates is not a random sample of the entire population of high school students. There are several reasons for this:

  1. Limited Demographic: Freda's classmates are likely to be a specific demographic group (students currently taking a statistics class), which may not reflect the views of all high school students. Statistics students might have a higher awareness or appreciation for math compared to students in other subjects or those who are not engaged in academic math paths.

  2. Self-Selection Bias: The fact that Freda’s sample consists only of her classmates could introduce bias, as students who are interested in statistics might share common views about math that don't necessarily reflect the opinions of the broader population of high school students.

Conclusion:

Because Freda's sample is not a random sample and is not a good representation of the overall population of high school students, she cannot confidently generalize her finding (82% believe that learning math is necessary) to all high school students.

Proposed Random Sample:

To obtain a more representative sample, Freda should consider conducting her survey in a way that includes a diverse and random selection of high school students. Here are some suggestions:

  1. Stratified Sampling: Divide the population of high school students into different strata based on relevant characteristics such as grade level, gender, socioeconomic status, and academic track (e.g., honors, general education, vocational). Then randomly sample students from each stratum.

  2. Random Sampling from Multiple Schools: Conduct the survey in various high schools in different districts to capture a broader range of opinions. She can use random selection techniques (like a random number generator) to choose students from different schools.

  3. Use Digital Platforms: Create an online survey and distribute it through school networks or social media platforms that target high school students. This method can reach a larger, diverse audience while maintaining anonymity.

By using a random sampling method, Freda would increase the likelihood of obtaining a more accurate representation of high school students' views on the necessity of learning math.