Question

Consider the following statement: A county tax assessor reported that the proportion of property owners who paid 2012 property taxes on time was 0.93 . 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, \(p=0.93\) or \(p=0.93 ?\)

Short answer

a. The number mentioned in the statement represents a population proportion. b. The correct use of notation is \(p=0.93\).

Step-by-step solution

Identification of the Proportion Type

The proportion provided in this exercise is referred to all property owners in the county who paid their 2012 property taxes on time, which makes it a population proportion. A population proportion refers to the whole set we're studying, whereas a sample proportion refers to a subset of the population. Thus, in this exercise, we're dealing with a population proportion because it talks about all property owners within the county, not just a subset of them.

Understanding of the Notation

In statistics, the population proportion is often denoted by 'p'. Therefore notation would be \(p=0.93\). However, in the exercise part b, two notations look almost same where first one is \(p=0.93\) and the second one is \(p=0.93?\). The question mark in the mathematical notation is not a valid symbol and could cause confusion. Hence, the appropriate and correct representation would be \(p=0.93\).