**What is it called when you take data from a random sample to draw conclusions about the rest of a population?** When you take data from a random sample to draw conclusions about the rest of a population, it's called *statistical inference.* **What are the two things you can do to learn from data?** The two things you can do to learn from data are: 1. Create estimates of population characteristics. 2. Perform hypothesis tests to answer questions or support claims about a population. **What types of calculations does statistical inference use?** The types of calculations that statistical inference uses are *ones based on probability theory.* **What is a P-value?** A P-value is *the probability that you'd get your observed results if the null hypothesis ($H_0$) were true.* **What are summary statistics used for in statistical estimation?** In statistical estimation, summary statistics are used *to approximate the value of an unknown population parameter and build a range of plausible values.* > [!example] Example of using summary statistics for statistical estimation > A sample mean ($\overline X$) is a single value calculated from a sample to estimate the mean for a population ($\mu$). A confidence interval built around said sample mean gives a range of values which we are confident contains the true population mean. > [!example] Example of hypothesis testing > Say you've calculated the mean amount of money that dog owners and cat owners spend on their pets. Your research question is, "Do dog owners spend more on their pets than cat owners do?" > > The null hypothesis would be, "There is no difference in spending per year on their pets between dog owners and cat owners." Written in mathematical notation, it would look like: > $H_0:\mu_\textrm{ Dog owners}=\mu_\textrm{ Cat owners}$ > The alternative hypothesis would be, "Dog owners spend more per year on their pets than cat owners." Written in mathematical notation, it would look like: > $H_A:\mu_\textrm{ Dog owners}>\mu_\textrm{ Cat owners}$ **What does a null hypothesis always propose?** A null hypothesis always proposes *no change or no difference.* **What does an alternative hypothesis always propose?** An alternative hypothesis always proposes *the research question or that something has changed.* **What is a test statistic used for?** A test statistic is used for *determining whether the data is consistent with the null hypothesis.* ...