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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

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Freda's sample is not a random sample and likely does not provide a good representation of the overall population of high school students. Since she surveyed her statistics classmates, the sample is limited to a specific group of students who are already enrolled in a statistics course. This group may have different attitudes toward math compared to the general population of high school students, who may include students from various backgrounds, interests, and academic levels.

Because her sample is biased towards students who are already studying statistics, the 82% finding cannot be generalized to all high school students. It's crucial in statistics to obtain a random and representative sample to draw conclusions about a larger population.

To improve her survey, Freda should consider the following random sampling methods:

  1. Stratified Sampling: Divide the population of high school students into strata based on characteristics such as grade level (freshmen, sophomores, juniors, seniors) or type of school (public, private, charter). Then, randomly select students from each stratum to ensure that various perspectives are included.

  2. Simple Random Sampling: Randomly select a number of students from a complete list of high school students within a certain geographic area, ensuring that every student has an equal chance of being selected.

  3. Cluster Sampling: Randomly select a few high schools and then survey all students within those selected schools. This can help reach a wider audience while still maintaining randomness in choosing the schools.

By using one of these sampling techniques, Freda can gather data that is more likely to reflect the true beliefs of the entire population of high school students regarding the necessity of learning math.