### Unit 5: Estimation and Hypothesis Testing

Estimation is the process of making predictions based on the best available information. Businesses employ estimation in order to help managers make decisions regarding the future. For example, if the CFO estimates profits will be lower next year, the CEO will consider cost-cutting measures to make up for the loss. Normally, companies do not want to pursue aggressive cost-cutting because it usually comes in the form of layoffs, which are bad for employee morale.

In order to make accurate estimates, companies use hypothesis testing. For example, assume the CFO thinks profits will be below 5% of revenue next year. His null hypothesis is that profits will be 5% or greater next year. The alternative hypothesis is that profits will not be 5% or greater next year. This seems counter-intuitive, but statistics proposes that a hypothesis cannot be proven true; it can only be rejected, or shown to be not true. Through the hypothesis testing process, the CFO will either reject or accept the null hypothesis. Hypothesis tests are always framed in this manner because, with imperfect information, nothing can be proven.

The best non-business analogy to hypothesis testing comes from the courtroom. In the United States, a defendant is presumed innocent until proven guilty. The null hypothesis in this scenario is innocent or not guilty. The alternative hypothesis is guilty. In order to find the defendant guilty, the jury must be offered enough evidence that suggests the defendant is guilty beyond a reasonable doubt. If the members of the jury make that decision, then they reject the null hypothesis. If the jury members decide they do not have enough evidence to make that judgment, then they must find the defendant not guilty. Notice not guilty does not mean the jury claims the defendant is innocent. The decision simply means the members of the jury do not have enough information to find the person guilty, so they err on the side of caution and fail to reject the null hypothesis. As an aside, in this example, beyond a reasonable doubt is analogous to the level of significance, which you will learn is crucial to hypothesis testing.

**Completing this unit should take you approximately 11 hours.**

Upon successful completion of this unit, you will be able to:

- estimate intervals over which the population parameter could exist;
- determine and differentiate between the null and alternative hypotheses in hypothesis testing;
- identify when to use the z and t distributions, and use these distributions to find probabilities;
- test hypotheses of the population mean and population proportion using one or two samples;
- define and apply the significance level, and explain its importance to hypothesis testing; and
- compute a test statistic and determine a region of acceptance based on a test statistic.

- estimate intervals over which the population parameter could exist;

### 5.1: Estimation and Confidence Intervals

Read this chapter, which discusses how to construct a confidence interval for a given population. Make sure you read the introduction as well as sections 8.1 through 8.4. Attempt the practice problems and homework at the end of the chapter.

Watch the first lecture from 1:05:00 to the end to learn more about confidence intervals and estimating parameters. Then watch the second lecture, which goes into more detail about confidence intervals and how to use them.

Read this section to learn how to compute confidence intervals for finding a range for the real population parameter using statistics from the sample data.

### 5.2: Hypothesis Testing

Watch this video, which explains how to test a hypothesis.

This chapter builds on your knowledge of confidence intervals to introduce you to the concept of hypothesis testing, which is how statisticians use the scientific method to learn more about the populations they are studying. Make sure you read the introduction as well as sections 9.1 through 9.4. Attempt the practice problems and homework at the end of each section.

Watch the first lecture from 1:12:00 to the end. In it, Professor Stark covers problems related to hypothesis testing. Then, watch the second lecture, in which Professor Stark goes through additional problems related to hypothesis testing.

### 5.3: Testing Equality of Two Percentages

Watch these videos, which explain how to compare the proportion of two different samples.

Read this chapter, which discusses how to compare data from two similar groups. This is useful when, for example, you want to analyze things like how someone's income relates to another sample that you are interested in. Make sure you read the introduction as well as sections 10.1 through 10.6. Attempt the practice problems and homework at the end of the chapter.

### 5.4: The Chi-Squared Test for Goodness of Fit

Watch these videos, which introduce chi-square tests and show when each kind of chi-squared test is used.

Read this chapter, which introduces you to the three major uses of the chi-squared distribution: the goodness-of-fit test, the test of independence, and the test of a single variance. Make sure you read the introduction as well as sections 11.1 through 11.6. Attempt the practice problems and homework at the end of the chapter.

### Unit 5 Problem Set and Assessment

Complete the problems in the practice section. To see a solution, click "Solution" beneath the problem.

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

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