Final answer:
In inferential statistics, an insurance company's study on malpractice lawsuits among doctors and a fitness center's survey on client exercise time are real-world examples where a sample statistic is used to infer a population parameter.
Step-by-step explanation:
In inferential statistics, real-world examples abound where a sample statistic is used to estimate a population parameter. For instance, an insurance company may wish to estimate the proportion of medical doctors involved in malpractice lawsuits. They could select a sample of 500 doctors from a directory and record how many have been sued for malpractice. The entire directory represents the population, the 500 doctors selected constitute the sample, the true proportion of doctors who have faced malpractice suits is the parameter, and the proportion in the sample of 500 is the statistic. The insurance company would then use this sample statistic to infer the parameter for the entire population of doctors.
Another illustration involves a fitness center interested in the average time clients spend exercising each week. If the fitness center surveys a group of its clients, the group is the sample, and the average time these clients report exercising is the statistic. This statistic provides an estimate of the parameter, which is the average time all clients of the center spend exercising each week. The value derived from the sample is thus used as an inference about the population parameter.