Question

1. Forty randomly-selected members of a high school music program were asked to report the number of hours they spend practicing each week. If you were to compute the mean number of hours, would you answer be a parameter or a statistic? Explain.

Answer 1

Answer: Statistic

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Explanation:

The fact that we have the phrasing "randomly-selected" in there is a big clue that we are working with a sample, and not a population. If 40 people represented the population, then we wouldn't be randomly selecting anyone. Everyone would be surveyed. No random process needed. We don't need to worry about the order of those surveyed.

However, we are applying a random selection process to form this sample. A statistic is some value that measures a sample. For instance, xbar is the sample mean which is a sample statistic. The xbar value estimates mu, which is a greek letter. Mu is the population mean and a population parameter.

To remember the difference between the two terms parameter and statistic, one useful memory trick is to think of it like this:

• Statistic and sample both start with s
• Population and parameter both start with p

As the name "statistics" implies, it is the study of how to estimate a population based on a sample. After gathering the sample, we compute a statistic, which in turn estimates a parameter. So that explains why your math course and textbook has that label.