Question

Consider the following statement: Fifty people were selected at random from those attending a football game. The proportion of these 50 who made a food or beverage purchase while at the game was \(0.83 .\) 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, \(p=0.83\) or \(\hat{p}=0.83 ?\)

Short answer

a. The number \(0.83\) in the statement is a sample proportion. b. The correct notation to use in this context is \(\hat{p} = 0.83\).

Step-by-step solution

Understanding sample proportion vs. population proportion

A sample proportion is derived from a subset or a 'sample' of the total population. It serves to give an estimate of the population proportion. On the other hand, a population proportion is derived when data from the entire population is considered. Therefore, in this case, since data has been collected from a random selection of 50 people attending the game and not from everyone, the proportion \(0.83\) represents a sample proportion.

Determining the correct notation for sample proportion

In statistical notation, 'p' is generally used to denote a population proportion, whereas '\(\hat{p}\)' is used to denote a sample proportion. Since the derived proportion is a sample proportion, the correct notation here is \(\hat{p} = 0.83\).