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. IT IS NOT A RANDOM SAMPLE explain: 1) What evidence do we have that tells us it is not a random sample.

Question

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. IT IS NOT A RANDOM SAMPLE explain: 1) What evidence do we have that tells us it is not a random sample.
2) Propose a way she could select a random sample of her population (students at her high school).

GPT-4o mini · Answer

Freda's survey of her statistics classmates does not constitute a random sample or a good representation of the entire population of high school students. Let’s break down the reasons why this is the case:

1) Evidence that it is not a random sample

Sample Bias: Freda's survey is limited only to her classmates in a statistics course. This group is likely to be comprised of students who have chosen to take statistics, potentially indicating a higher interest or aptitude in mathematics compared to the general high school population. Therefore, they may have a biased view on the necessity of learning math based on their academic background.
Limited Diversity: The classmates may not represent the broader diversity of the entire high school student body in terms of interests, future career goals, or fields of study. Students who are not mathematically inclined or are pursuing non-STEM fields may have different opinions on the importance of math.
Sample Size and Homogeneity: The sample size is likely small and homogeneous, as it consists of students from a specific course rather than a cross-section of the school. This homogeneity further skews the results.

2) Proposing a way to select a random sample

To achieve a random sample of all high school students, Freda could use the following method:

Stratified Random Sampling: Freda should divide the entire student body into distinct strata or groups based on factors such as grade level (9th, 10th, 11th, 12th) or academic tracks (e.g., college prep, vocational). Then, from each group, she could randomly select students to participate in her survey. This approach ensures representation from each segment of the population.
Random Selection Process: Freda could achieve this by:
1. Obtaining a list of all students at her high school (which might be available from the school administration).
2. Assigning each student a unique identifier (like a student ID number).
3. Using a random number generator to select a predetermined number of student IDs from the list, ensuring that each student has an equal chance of being selected.

By employing this random selection method, Freda would be able to gather a more representative sample of the high school population, leading to more reliable conclusions about the proportion of high school students who believe learning math is necessary.