**Module Three**

One of the primary purposes of statistical research is to provide information to support decisions that are to be made. Researchers, statisticians, and even you are asked to provide information about a variety of population parameters. For example, Georgia's Public Broadcasting System (PBS) may want to know how many Georgians watch their programs each week. But it is impossible to survey each and every household in Georgia; yet, PBS needs the best information as possible to make programming decisions. This is were **Inferential Statistics** is important!

Recall from Module One that **Inferential Statistics** is the branch of statistics that uses sample data to make generalizations about a population parameter. While there are a variety of sample statistics that could be used to provide estimates for the population parameter, in this module, we will focus on two options that researchers and statisticians use to make "statistical inferences" (generalizations) about populations based on samples take from the population.

The first option is the Confidence Interval, which determines a range of values for the population mean, rather than a single point estimate (value). (We found point estimates in Module 2)

The second option is Hypothesis Testing, which is a process researchers and statisticians use to determine if a proposed solution to a question is valid or invalid, on target or not.

This module contains some of the hardest material that we cover; however, it is some of the MOST important as well.

**Overview of the Module **

- Central Limit Theorem
- Confidence Intervals for Z-interval and T-interval
- Hypothesis Testing
- One mean z-Test
- One mean t-test

**COURSE OBJECTIVES**

The student will be able to:

- Demonstrate fundamental concepts in exploratory data analysis
- Describe the concept of the sampling distribution of a statistic, and characterize the behavior of the sample means
- Utilize the foundations of inferential statistics involving confidence intervals and hypothesis testing
- Communicate and present statistical ideas clearly in oral and written forms using appropriate technical terms and deliver data analysis results to non-statistical audience.

**MODULE THREE OBJECTIVES**

The student will be able to

- Use an appropriate software tool for data summary and exploratory data analysis
- Describe properties of the sampling distribution of the sample mean
- Calculate a confidence interval (z, t)
- Interpret a confidence interval (z, t)
- Identify the components of a hypothesis test including the parameter of interest, the null and alternative hypotheses, and the test statistic
- One-mean z-test
- One-mean t-test

- Compute the p-value of a test statistic