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.
5.1: Estimation and Confidence Intervals
5.2: Hypothesis Testing
5.3: Testing Equality of Two Percentages
5.4: The Chi-Squared Test for Goodness of Fit
Unit 5 Problem Set and Assessment