Math Problem Statement

A Quest Diagnostics analysis of 10 million drug tests of adults in the United States revealed that 4.22​% of the tests were positive for illegal drugs. Identify the population and the sample. Is the value of 4.22​% a statistic or a​ parameter?

Solution

In this problem:

  • Population: The population refers to the entire group of individuals or instances about which we want to draw conclusions. Here, the population is all adults in the United States.

  • Sample: The sample is the subset of the population that is actually observed or analyzed. In this case, the sample consists of the 10 million adults in the United States whose drug tests were analyzed by Quest Diagnostics.

  • 4.22%:

    • Since this value is derived from the sample of 10 million adults, it is a statistic.
    • If the percentage represented the entire population of adults in the U.S., it would be considered a parameter. However, because it is calculated from a sample, it is a statistic.

Summary:

  • Population: All adults in the United States.
  • Sample: The 10 million adults in the United States who were tested.
  • 4.22%: This is a statistic because it is based on a sample.

Would you like further details or have any questions?


Related Questions:

  1. What is the difference between a statistic and a parameter?
  2. How is a sample chosen from a population?
  3. What are some common methods for ensuring a sample is representative of the population?
  4. What are the potential sources of bias in drug testing studies?
  5. How might the results differ if the entire population were tested instead of just a sample?

Tip: Always distinguish between a statistic and a parameter by remembering that statistics come from samples, while parameters pertain to populations.

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Math Problem Analysis

Mathematical Concepts

Statistics
Sampling

Formulas

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Theorems

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Suitable Grade Level

College