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."

This question is asking us to use a simulation in order to determine whether or not an observed phenomenon is statistically probable. We will do this by creating and testing a hypothesis. Afterwards, we can use our collected data to make a conclusion as to whether or not Joe is using fair dice in this scenario. 

Hypotheses are "if/then" statements that represent an inference or educated guess regarding a particular phenomenon. They are tested through experimentation. The results of an experiment will reveal if a hypothesis can be supported or not. At this point, it is important tot note that a hypothesis can never be proven: experimentation can only support or refute a hypothesis. Even scientific theories cannot be proven they only have a mass of supporting studies to add to their scientific validity. 

Before we solve this problem, we should review the scientific process. In the scientific method we observe a phenomenon, gather background information, develop a tentative explanation (i.e. a hypothesis), test this explanation through the observation and manipulation of variables, and, finally, we create conclusions based upon experimentation. These conclusions will either support or refute the hypothesis.

Now, let's use this information to solve the problem regarding whether or not Joe is using fair dice. In this problem, Melissa noticed that Joe rolled snake eyes three times in a row. She gathered background information and identified the following probability calculations:

From this information, she realized that the probability of rolling snake eyes three times in a row is very low. Using this information, Melissa created an experiment, In this experiment, she rolled her known fair dice three times in a row for sixty trials. In these sixty trials she was only able to roll snake eyes in a row two times. From this information she was able to make the following conclusion: "Joe has tricked her by using loaded dice."

In this lesson we have learned how to use simulations and the scientific method in order to determine whether or not an event is the product of random chance or manipulation (i.e. Joe tricking Melissa with loaded dice).