Question

Consider the following statement: The Department of Motor Vehicles reports that the proportion of all vehicles registered in California that are imports is \(\mathbf{0} .22\). a. Is the number that appears in boldface in this statement a sample proportion or a population proportion? b. Which of the following use of notation is correct, \(p=0.22\) or \(\hat{p}=0.22 ?\) (Hint: See definitions and notation on page 363 )

Short answer

a. The number given, 0.22, is a population proportion. b. The correct notation to use is \(p=0.22\).

Step-by-step solution

Identify whether the given value refers to a sample or population proportion

The proportion given, 0.22, represents all vehicles registered in California that are imports. Since it refers to all vehicles in California, this is a population proportion, not a sample proportion.

Appropriate Notation

In the context of the given problem, the correct notation to use would be \(p=0.22\) because as established, 0.22 refers to a population proportion. It's crucial to note that \(p\) is used for population proportions, while \(\hat{p}\) is used for sample proportions.