EXAMPLE 14 Working Hard and Getting Ahead: A Sample Statistic

The actual results from the poll discussed at the start of this section were that 885 of the 1484 people who answered the question agreed with the statement “Most people if they want to get ahead can make it if they work hard.” (Notice not all of the 1500 people surveyed answered this question.) The proportion of the respondents who agreed was

The symbol is read “p-hat.” The ^ symbol here tells us that a quantity has been estimated, just as the use of in Chapter 6 (page 253) told us that a value was estimated by using a regression-line model. The number is a statistic. The corresponding parameter is the proportion (call it ) of all adult U.S. residents who would have responded “Agree” if questioned about the same statement. We don’t know the value of the parameter , so we use the statistic to estimate it.