Question

Fans of professional soccer are probably aware that players sometimes fake injuries (called dives or flops). But how common is this practice? The articles "A Field Guide to Fakers and Floppers" (Wall Street Journal, June 28,2010 ) and "Red Card for Faking Footballers" (Science Daily, Oct. 10,2009) describe a study of deceptive behavior in soccer. Based on this study, it was possible to categorize injuries as real or fake based on movements that were characteristic of fake injuries (such as an arched back with hands raised, which is meant to attract the attention of a referee but which is not characteristic of the way people fall naturally). Data from an analysis of a sample of soccer games were then used to make the following statements: On average, referees stop a soccer game to deal with apparent injuries 11 times per game. \- On average, there is less than one "real" injury per soccer game. Are the inferences made ones that involve estimation or ones that involve hypothesis testing?

Short answer

The first statement is likely a result of estimation, as it provides an average value, typical for estimation. The second statement seems to be an outcome of hypothesis testing, as it presents a claim or assumption rather than a clear-cut value. It implies that the researchers may have tested a hypothesis about the true injury rate based on their sample data.

Step-by-step solution

Understand estimation

A process of estimation involves making an approximation or a guess about a population parameter based on a sample. It could be the case with the first inference - the referees stop a game to deal with injuries about 11 times per game. This might be an estimate based on the data from the sample of soccer games.

Understand hypothesis testing

Hypothesis testing is a procedure that includes making assumptions about the population parameter and then testing the validity of those assumptions based on the sample data. We can relate this to the second inference that there is less than one real injury per soccer game. It seems more like an assumption about the population parameter i.e., the count of real injuries per game, and then the sample data might have been used to test the validity of this claim.

Concluding the exercise

The first and second inferences seem to be results of estimation and hypothesis testing respectively. As we have no further information regarding how the researchers reached these figures, it is a reasonable conclusion based on common statistical practices.