Question

Consider the following statement: In a sample of 20 passengers selected from those who flew from Dallas to New York City in April 2012, the proportion who checked luggage was \(\underline{0.45}\). 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, \(p=0.45\) or \(\hat{p}=0.45 ?\)

Short answer

a. The number 0.45 represents a SAMPLE proportion. b. The correct notation is \(\hat{p}=0.45\).

Step-by-step solution

Interpretation of the statement

In the statement, it is mentioned that a 'sample of 20 passengers' was taken out of those who traveled from Dallas to New York in April 2012. This implies that the number 0.45 is a calculation based on a subgroup or sample out of the total population of passengers. Hence, the proportion 0.45 represents a sample proportion.

Correct notation selection

Since the proportion represents a sample proportion, the correct notation to use is \(\hat{p}=0.45\). Here, \(\hat{p}\) denotes a sample proportion, as opposed to p which is generally used for a population proportion.