Explain how the psychologist is using statistical estimation in this study. In your explanation, identify the specific group and value that represent the sample statistic, and the larger group and value that represent the population parameter.
Case context: A clinical psychologist is studying self-esteem levels in teenagers diagnosed with social anxiety. The psychologist selects a specific group of teenagers with social anxiety and calculates their average self-esteem score. The psychologist then uses this calculated average score to draw conclusions about the true average self-esteem score for all teenagers diagnosed with social anxiety.
Question: Explain how the psychologist is using statistical estimation in this study. In your explanation, identify the specific group and value that represent the sample statistic, and the larger group and value that represent the population parameter.
Sample answer: The psychologist calculates the average self-esteem score from a specific group of teenagers, which serves as the sample statistic. This statistic is then used to estimate the corresponding population parameter, which is the true average self-esteem score for all teenagers diagnosed with social anxiety. The psychologist is using the known sample statistic to draw conclusions about the unknown population parameter.
Key points:
- Explain that the psychologist calculates a statistic from a specific group to estimate the larger population parameter.
- Identify the average self-esteem score of the teenagers as the sample statistic.
- Identify the true average self-esteem score of all teenagers diagnosed with social anxiety as the population parameter.
Rubric: The response must demonstrate comprehension by: 1. Explaining that the psychologist calculates the statistic from a subset to estimate the larger group's parameter. 2. Identifying the average self-esteem score of the specific group of teenagers as the sample statistic. 3. Identifying the true average self-esteem score of all teenagers diagnosed with social anxiety as the population parameter.
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