EXAMPLE 11Descriptive statistics or statistical inference?
State whether the following situations illustrate the use of descriptive statistics or statistical inference.
In Baltimore County, Maryland, the average amount spent per week on gasoline consumption in a sample of 500 commuters was $75. The county government infers that the average amount spent weekly by all Baltimore County commuters is $75.
A sample of 100 residents of Broward County, Florida, yielded 27 residents who work for the government at the local, state, or federal level. Thus, 27% of these 100 residents work for the government.
The average age of a sample of 200 residents of Garden City, New York, was 34 years old.
In a survey of 1000 citizens in the Seattle, Washington, metropolitan area, 570 said they would pay higher prices in order to reduce greenhouse emissions. City planners conclude that 57% of all Seattle citizens would do so.
Solution
Statistical inference. A sample was taken, and a sample statistic ($75 per week) was calculated. Then the county government used this statistic to make the statistical inference that this was the average amount spent by all Baltimore County commuters.
Descriptive statistics. Though a sample was taken, there was no attempt to make an inference from this sample of 100 workers to the entire population of Broward County, Florida. So, no statistical inference is being made here.
Descriptive statistics. The average age of 34 years old is a descriptive statistic, because it describes the sample. However, no inference is made regarding a larger population.
Statistical inference. The survey found that 57% of the sample of 1000 citizens would pay higher prices in order to reduce greenhouse emissions. This 57% is a statistic. Then the city planners used this statistic in order to perform statistical inference about the population of all Seattle citizens.