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A study is made to determine whether taking AP Statistics in high school helps students achieve higher GPAs when they go to college. In comparing records of 200 college students, half of whom took AP Statistics in high school, it is noted that the average college GPA is higher for those 100 students who took AP Statistics than for those who did not. Based on this study, guidance counselors begin recommending AP Statistics for college-bound students. Which of the following is incorrect? (A) While this study indicates a relation, it does not prove causation. (B) There could well be a confounding variable responsible for the seeming relationship. (C) Self-selection here makes drawing the counselors' conclusion difficult. (D) A more meaningful study would be to compare an SRS from each of the two groups of 100 students. (E) This is an observational study, not an experiment.

Step by step solution

01

- Understand the Types of Studies

First, identify the type of study described: According to the problem, the study is observational because the researchers observed existing conditions without controlling any variables.

02

- Analyze Each Statement Given

Read and analyze each option provided to identify incorrect statements based on the characteristics of observational studies:

03

Step 2.1 - Analyze Option (A)

Option (A): 'While this study indicates a relation, it does not prove causation.' This statement is correct. Observational studies can show correlation but cannot prove causation.

04

Step 2.2 - Analyze Option (B)

Option (B): 'There could well be a confounding variable responsible for the seeming relationship.' This statement is correct because confounding variables can affect the results in observational studies.

05

Step 2.3 - Analyze Option (C)

Option (C): 'Self-selection here makes drawing the counselors' conclusion difficult.' This statement is correct. Self-selection can bias the results because students who choose to take AP Statistics might have other beneficial characteristics.

06

Step 2.4 - Analyze Option (D)

Option (D): 'A more meaningful study would be to compare an SRS from each of the two groups of 100 students.' This statement is incorrect. An SRS helps reduce bias, but because the study is observational, it still cannot prove causation.

07

Step 2.5 - Analyze Option (E)

Option (E): 'This is an observational study, not an experiment.' This statement is correct. Observations are made without manipulation of the study environment, making it an observational study.

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Key Concepts

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

correlation vs causation

In statistics, it's important to differentiate between correlation and causation. Correlation means that two variables have a relationship, where changes in one variable are associated with changes in the other. However, this does not imply that one variable causes the other to change.
For instance, the study indicates that students who took AP Statistics in high school tend to have higher GPAs in college. This is a correlation. But, we cannot conclude that taking AP Statistics *causes* higher GPAs. Other factors might be at play, which leads us into our next topic.

confounding variables

Confounding variables are other variables that might influence both the supposed cause and effect. These variables can create a false impression of a relationship between the studied variables.
In our example, students who choose to take AP Statistics might also be those who have better study habits or higher motivation, which are confounding variables. These additional factors could be the real reasons behind their higher GPAs, not just the fact that they took AP Statistics.
Confounding variables make it difficult to determine the true cause of an observed effect, especially in observational studies.

self-selection bias

Self-selection bias occurs when individuals select themselves into a group, causing a potential bias in the sample. This is common in observational studies.
In the provided study, the students who elected to take AP Statistics might inherently differ from those who did not in ways that affect their GPA. For example, they might be more academically inclined or have more supportive educational backgrounds. Because of this self-selection, it's challenging to claim that taking AP Statistics alone is responsible for their higher GPAs.
Self-selection bias can significantly distort the results of a study by introducing variables that were not controlled or accounted for in the analysis.

observational study

An observational study involves observing subjects and measuring variables without assigning treatments to the subjects. This contrasts with experimental studies where scientists manipulate the variables or conditions.
The study in question is observational because it compares the GPAs of students who chose to take AP Statistics with those who did not, without intervening in any way. Observational studies can reveal associations but cannot establish causation due to lack of control over extraneous variables.
Observational studies are useful for exploring relationships and generating hypotheses, but they have limitations in proving cause-and-effect due to the presence of confounding variables and biases.