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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% of them believe it is necessary to learn math. Is Freda’s sample a random sample and a 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 on which Freda should be conducting her survey.(4 points)

1 answer

Freda's sample likely is not a random sample nor a good representation of the entire population of high school students for a few reasons:

  1. Sample Composition: Freda is surveying her statistics classmates, which may not represent the diversity of opinions found in the broader high school population. Students in a statistics class might have different attitudes toward math compared to high school students at large, possibly skewing the results.

  2. Selection Bias: The classmates she surveyed might share similar backgrounds, interests, or academic strengths, which could influence their opinions. Since they are taking a statistics course, they may have a more favorable view of math compared to peers who are not engaged in such a class.

Given these points, her sample may not accurately reflect the views of all high school students regarding the necessity of learning math.

To improve the representativeness of her sample, Freda should consider conducting her survey in the following way:

  1. Stratified Random Sampling: She could randomly select students from different high schools in her area to get a variety of opinions. This ensures that the sample includes students from different backgrounds, academic levels, and perspectives.

  2. Random Selection Across Different Classes: Instead of only surveying classmates from her statistics course, she could also survey students from different subjects across various grades. For instance, she might randomly select students from math classes, science classes, humanities, and arts classes.

  3. Inclusion of Diverse Schools: To further reduce bias, Freda could include students from public schools, private schools, charter schools, and magnet schools to ensure a broad representation.

By adopting this approach, Freda would be able to gather a more reliable data set that could lead to more valid conclusions about the proportion of high school students who believe that learning math is necessary.