Andrew Believes The Honor Roll Students At His School Have A

1andrew Believes The Honor Roll Students At His School Have An Unfair

Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He surveyed 500 students, asking two questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are summarized in a contingency table showing the number of students in each category. To determine if all students have an equal opportunity to get their requested math class, Andrew needs to analyze whether being on the honor roll influences the likelihood of getting the requested class. This involves statistical hypothesis testing, specifically a chi-square test of independence, which assesses whether the variables "honor roll status" and "received requested math class" are independent or not. By calculating expected frequencies based on marginal totals and comparing them with observed frequencies, Andrew can ascertain if a significant association exists. If the test indicates dependence, then honor roll status may give students an unfair advantage, suggesting the process is biased. Conversely, if the variables are independent, opportunities are equitable across students regardless of honor roll status.

Paper For Above instruction

Determining whether students at a school have an equal opportunity to get their requested math class requires careful statistical analysis. The most suitable method is conducting a chi-square test of independence using the data gathered from the survey. This test evaluates if the variables "honor roll status" and "getting the requested math class" are related or independent. If they are dependent, it implies that being on the honor roll influences the probability of obtaining the desired class, indicating an unfair advantage. If independent, all students have equal opportunities regardless of honor roll status.

To perform the chi-square test, Andrew must first organize the data into a contingency table with four categories: honor roll students who received their requested class, honor roll students who did not get their requested class, non-honor roll students who received their requested class, and non-honor roll students who did not get their requested class. Using the totals from the survey, expected frequencies under the assumption of independence are calculated by multiplying the marginal totals for each row and column and then dividing by the total number of students surveyed. Comparing these expected counts with the observed data reveals whether the differences are statistically significant.

If the calculated chi-square statistic exceeds the critical value from the chi-square distribution table at a chosen significance level (commonly 0.05), then the null hypothesis of independence is rejected. This means that honor roll status does impact the likelihood of obtaining the requested math class, pointing to an unfair advantage for honor roll students. Conversely, if the chi-square statistic is below the critical value, then the data do not provide enough evidence to suggest dependence, indicating that the class assignment process is fair to all students regardless of honor roll status. This statistical analysis allows Andrew to make an evidence-based conclusion about fairness in class assignments at his school.

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