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Consider the following graphical display that appeared in the New York Times: Based on the data summarized in the graph, we can see that students who have a high school GPA or 3.5 or higher and a combined SAT score of over 1200 have an \(89 \%\) graduation rate when they attend a "most selective" college, but only a \(59 \%\) graduation rate when they attend a "least selective" college. Give an example of a potential confounding variable that might explain why the following statement is not reasonable: If all the students that have a GPA of 3.5 or higher and a combined SAT score of 1200 or higher and that were admitted to a "least selective" college were moved to a "most selective" college, the graduation rate for these students would be approximately \(89 \%\)

Step by step solution

01

Understanding the Concept of Confounding Variable

A confounding variable is an outside influence that changes the relationship between an independent variable (in this case, choosing a selective or non-selective school) and a dependent variable (here, the graduation rate).

02

Identifying a Potential Confounding Variable

A potential confounding variable in this scenario could be individual student motivation. Students with higher GPAs and SAT scores may be more motivated to succeed in school, which could lead to higher graduation rates. However, their motivation, not the school's selectiveness, may be the primary reason they're more likely to graduate. Thus, simply moving less motivated students from a less selective school to a more selective college might not automatically increase their graduation rates.

03

Evaluating the Effect of the Confounding Variable

If the motivation is indeed a major confounding variable in this scenario, it would undermine the argument that simply transferring students from a 'least selective' to a 'most selective' college would boost their graduation rates to around 89%. Even if these students were in a more challenging environment, without the necessary motivation, they might not achieve the expected graduation rate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Graduation Rates

Graduation rates are the percentages of students who complete their degree programs within a specified timeframe. Generally, for undergraduate programs, a common measure is the percentage of students who graduate within six years of starting. These rates can indicate the effectiveness of a college in helping students to achieve their academic goals.

Graduation rates are often used as a marker of a college's success. Higher rates suggest that the institution may provide a supportive learning environment, offer adequate resources, and ensure that students remain engaged until they graduate. Such factors can play a significant role in ensuring students do not drop out mid-program.

• Graduation rates vary depending on various factors like the selectiveness of a college.
• They can also be influenced by external aspects like financial aid availability and student support services.
• High graduation rates could indicate good academic advising and tutoring services, apart from motivated student cohorts.

Selective Colleges

Selective colleges are institutions that admit only a small percentage of applicants, often basing this selection on criteria such as high school GPA, SAT/ACT scores, and other achievements. This selectiveness can lead to a perception of higher academic standards and prestige.

These colleges tend to have high graduation rates, but it's crucial to note that this isn't solely due to their selectivity. They often attract highly motivated students who are capable of meeting the demands of rigorous academic programs.

• Selective colleges often offer ample resources, such as experienced faculty and research opportunities.
• The competitive nature of these institutions can foster a motivated cohort of students who push each other to succeed.
• They may also provide extensive career services, facilitating smoother transitions to post-college life for graduates.

Student Motivation

Student motivation can be a significant driving force behind academic success and completion of a program. Highly motivated students tend to set personal goals and persist in reaching them, regardless of their academic environment.

In the context of the graduation rates discussed, motivation can serve as a confounding variable. That means it might be impacting graduation rates more significantly than the selectiveness of the college itself.

• Motivation influences students' drive to seek help, join groups, and make use of resources.
• It leads to better time management, allowing students to balance academic and extracurricular activities.
• This internal drive can sometimes outweigh institutional factors, suggesting that a motivated student might perform well in both selective and less selective colleges.