Introduction to Inferences
So far, we learned how to collect and summarize data (Lesson 1). Then we learned how to quantify the likelihood of events using probability (Lesson 2). Next, we learned how to model these events as random variables (Lesson 3). In the previous Lesson, we learned how to find the sampling distributions of sample statistics (Lesson 4).
In Lesson 4, the sampling distributions for the sample statistics assumed we knew the population parameters (fantasy land). In real life, we do not know these parameters (or we would not need statistics!). In this lesson, we switch from "fantasy land" to real life. We know what to do when the parameters are known, let's see how we can use that information when they are unknown.
- Describe the role of statistical inference in estimation in terms of the population and sample.
- Explain the general form of a confidence interval and apply it to different statistics and conditions.
- Construct a confidence interval to estimate a population mean or proportion.
- Given a confidence interval, interpret the meaning in terms of the population.
- Identify when to use the t-distribution as opposed to the normal distribution given the sample size and population distribution.
- Define and interpret the margin of error.
- Given the population standard deviation and a confidence level, calculate the required sample size needed to obtain the desired margin of error.