Topic: 2021FRQ真题详解

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重要考点：

1. the random variable of interest in statistics

• Unknown but Measurable: Random variables represent something we can't know for sure (like the next roll of a dice), but we can assign numbers to the possible outcomes (1, 2, 3, etc. for the dice).

• Types of Random Variables: There are two main categories:
• Discrete: These variables can only take on specific, separate values. Examples include the number of customers in a store (1, 2, 3, ...) or the results of a coin toss (heads, tails).
• Continuous: These variables can take on any value within a certain range. Examples include weight, height, or time it takes to complete a task.

• Understanding Probabilities: By using random variables, we can analyze the probability of different outcomes occurring. This allows us to understand the likelihood of certain events and make predictions based on statistical models.

2.confounding variable

1. Effect of Exercise on Weight Loss: In a study examining the relationship between exercise and weight loss, diet can act as a confounding variable. If not controlled for, differences in diet could influence weight loss, making it seem as though exercise had a greater or lesser effect than it truly does.

2. Smoking and Lung Cancer: In early studies investigating the link between smoking and lung cancer, air pollution could be considered a confounding variable. If air pollution levels were not taken into account, the study might not accurately reflect the risk of lung cancer associated with smoking alone, as both smoking and high levels of air pollution are risk factors for lung cancer.

3. Medication and Recovery Time from Illness: Suppose a study aims to determine whether a new medication reduces recovery time from a certain illness. The overall health status of participants could serve as a confounding variable. Healthier individuals might recover more quickly regardless of the medication, suggesting that the medication is more effective than it actually is if the health status is not controlled for.

4. Education and Income: In exploring the relationship between education level and income, work experience could act as a confounding variable. Without accounting for work experience, it might appear that higher education directly leads to higher income, when in reality, those with more work experience (which often correlates with age) might naturally have higher incomes.