All Common Core: High School - Statistics and Probability Resources
Example Question #1 : Making Inferences About Population Parameters From Random Sample: Ccss.Math.Content.Hss Ic.A.1
A car designer wants to know if customers prefer automatic or manual transmissions in cars. The designer hires a market research team to randomly sample and survey the preferences of potential car buyers in three major cities: New York, Chicago, and Los Angeles.
The data collected in this survey would be best described as which of the following?
None of these
Solving questions related to this standard requires an understanding of definitions common to statistics. Specifically, this question is testing your knowledge of the difference between two fundamental statistical concepts: sample statistics and population parameters. Let's begin by discussing the differences between these two measures. Later, we will use this information to solve the problem.
First let's discuss what is meant by the term population. In statistics, a "population" is described as the entire group that is to be studied. An example of a population in the natural sciences would be every giant panda of the species Ailuropoda melanoleuca in the wild (1864 individuals according to the World Wildlife Foundation)—not captivity. Now, let's identify what is meant by the term population parameter. A "population parameter" is a statistic that is found by sampling the entire population. For example, the mean weight of the entire wild population of giant pandas in the world would be an example of a population parameter (i.e. the mean weight of all 1864 pandas). Next, we will discuss sample populations and statistics.
A "sample" is the subset of a population that is being studied. For example, researchers for a university want to study giant pandas in the wild but can only access a group of 100 pandas sampled in Sichuan, China. Data collected from this particular study would be known as a sample statistic (e.g. the mean weight of pandas in the Sichuan region). It is important to note that the external validity of some sample statistics are hindered. The external validity of a statistic is its ability to be applied to other samples and remain valid. If locals fed pandas in the Sichuan region, then their mean weight may be greater than those of the southern or northern regions. In this instance, the mean would not be representative of other populations of giant pandas.
Last, we should note that certain sample populations are better than others at predicting population parameters. A population parameter can be considered to be the true statistic of a given population while a sample statistic is only an estimate of a part or subset of the population. Simple random samples are good predictors of population parameters and can be used to estimate them. They are collected when every member in a population has an equal chance of being chosen (e.g. randomly selecting 100 of the 1864 pandas in the world).
Now, let's use this information to solve the question. The designer wants to know the preferences of potential car buyers; however, he only samples three major US cities. The data collected from this survey is an example of a sample statistic. It did not gather information from all of the potential car buyers for the particular company; therefore, the best answer is "sample statistic."