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Chapter 7: Problem 27

Suppose that, when taking a random sample of three students' GPAs, you get a sample mean of \(3.90 .\) This sample mean is far higher than the collegewide (population) mean. Does that prove that your sample is biased? Explain. What else could have caused this high mean?

Short Answer

Expert verified
No, the high sample mean doesn't necessarily prove that the sample is biased. Such a high sample mean could be as a result of random variation or due to other factors, such as non-random selection or the higher performance of certain cohorts within the population.

Step by step solution

01

Understanding Sample Mean and Population Mean

Sample mean is the average value of a subset or 'sample' from a population. In this scenario, it refers to the average GPA of three random students. The population mean, on the other hand, represents the average GPA of the entire college. A difference in these two values doesn't necessarily indicate a biased sample.
02

Interpreting the Difference between Sample and Population Mean

The fact that the sample mean GPA of 3.90 is far higher than the population mean might simply be an instance of random variation. The three students chosen for this sample could randomly happen to have exceptionally high GPAs, raising the sample mean.
03

Considering Other Possible Factors

Other than statistical randomness, there could be other factors causing a high mean. For example, if the sample is not randomly selected and instead picked from a group of top-performing students, the sample would be biased. Similarly, if the sample happens to only include third-year or fourth-year students who generally have higher GPAs, this could also cause a higher mean.

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Most popular questions from this chapter

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