Understands and applies inferential statistics
Statistical inference is the process of using a sample to draw conclusions (make inferences) that go beyond the sample. Since the sample does not contain all the information about the population or all the results from all possible experiments, probability is used to help describe the limitations of the inference. For example, in an experiment to test the relative effectiveness of two drugs, the inference that one is better than the other is qualified by using probability to describe how likely it is that the results of the experiment are due to chance rather than effectiveness of the drug.
Students should be able to take information from a sample and make basic inferences beyond the sample, for example inferences about the relative effectiveness of two treatments and inferences from a sample to a population. Instruction should start with activities involving simulations and should address issues of experimental design, randomness, rare events, sources of bias, and sample size. Building on the use of simulation, students should understand key ideas such as sampling distribution and rare event, and use these ideas to analyze and interpret confidence intervals and hypothesis tests.
Inferential statistics is often part of a statistical study. A statistical study is a survey, experiment, or observational study that applies statistical thinking. Statistical thinking involves formulating questions, collecting data relevant to those questions, analyzing the data, and drawing appropriate conclusions. Students should be able to apply statistical thinking to analyze, design, and conduct simple statistical studies. In doing so, they will use descriptive statistics, statistical inference, and probability.