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Chapter 7: Problem 6

Two symbols are used for the standard deviation: \(\sigma\) and s. a. Which represents a parameter, and which represents a statistic? b. To estimate the commute time for all students at a college, 100 students are asked to report their commute times in minutes. The standard deviation for these 100 commute times was \(13.9\) minutes. Is this standard deviation \(\sigma\) or s?

Short Answer

Expert verified
a. \(\sigma\) represents a parameter and 's' represents a statistic. b. In the given scenario, the standard deviation is represented by 's'.

Step by step solution

01

Understand the Terms

The two key terms involved here are 'Parameter' and 'Statistic'. Parameter is a characteristic that describes a population, while Statistic is a characteristic that describes a sample.
02

Identification of Symbols

In statistical language, the symbol \(\sigma\) represents the standard deviation of a population, which is a parameter. Meanwhile, 's' symbolizes the standard deviation of a sample, which is a statistic.
03

Apply the Knowledge to Given Scenario

In the scenario given, 100 students from a college reported their commute times in minutes. This group of students represents a sample from the overall population of all students at the college. Therefore, the standard deviation in this case would be represented by 's', not \(\sigma\).

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