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Chapter 7: Problem 5

Two symbols are used for the mean: \(\mu\) and \(\bar{x}\). a. Which represents a parameter, and which a statistic? b. In determining the mean age of all students at your school, you survey 30 students and find the mean of their ages. Is this mean \(\bar{x}\) or \(\mu\) ?

Short Answer

Expert verified
a. \(\mu\) represents a parameter while \(\bar{x}\) represents a statistic. b. The mean determined by surveying 30 students would be \(\bar{x}\), as it is a sample mean, not a population mean (\(\mu\)).

Step by step solution

01

Understand the Definitions

Firstly, understanding the two crucial terms, 'parameter' and 'statistic' is essential. A 'parameter' is a value which describes a characteristic of an entire population, whereas a 'statistic' is a quantity calculated from a sample of data, it estimates or gives information about a population parameter.
02

Identify the Symbols

The symbol \(\mu\) represents the 'population mean', which is a parameter. While \(\bar{x}\) represents the 'sample mean', which is a statistic. It is used when trying to estimate the true mean (\(\mu\)) of the entire population based on a sample.
03

Apply Knowledge to Situation

In the case of determining the mean age of all students at school, if you survey 30 students and find the mean of their ages, this mean would correctly be represented by \(\bar{x}\), since it is based on a sample, not the entire population.

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Most popular questions from this chapter

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