8-1 Basics of Hypothesis Testing 377 Importance of Terminology This chapter introduces several terms that should be known because they are the same terms used in many different fields, not just statistics. For example, when learning the meaning of “null hypothesis” and “alternative hypothesis” and “P-value,” you are learning terminology used in medicine, advertising, criminology, law, and many other disciplines. These terms are not unique to statistics. Steps 1, 2, 3: Use the Original Claim to Create a Null Hypothesis H0 and an Alternative Hypothesis H1 The objective of Steps 1, 2, 3 is to identify the null hypothesis and alternative hypothesis so that the formal hypothesis test includes these standard components that are often used in many different disciplines. The null hypothesis includes the working assumption for the purposes of conducting the test. DEFINITIONS The null hypothesis (denoted by H0) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is equal to some claimed value. The alternative hypothesis (denoted by H1 or Ha or HA) is a statement that the parameter has a value that somehow differs from the null hypothesis. For the methods of this chapter, the symbolic form of the alternative hypothesis must use one of these symbols: 6, 7, ≠. HINT Think of the null hypothesis as a “working assumption” (that you may or may not believe). The term null is used to indicate no change or no effect or no difference. We conduct the hypothesis test by assuming that the parameter is equal to some specified value so that we can work with a single distribution having a specific value. Example: Here is an example of a null hypothesis involving a proportion: H0: p = 0.5 Example: Here are different examples of alternative hypotheses involving proportions: H1: p 7 0.5 H1: p 6 0.5 H1: p ≠ 0.5 Given the claim from Example 1 that “most Internet users utilize two-factor authentication to protect their online data,” we can apply Steps 1, 2, and 3 in Figure 8-1 as follows. Step 1: Identify the claim to be tested and express it in symbolic form. Using p to denote the probability of selecting an Internet user utilizing two-factor authentication, the claim that “most Internet users utilize two-factor authentication” can be expressed in symbolic form as p 7 0.5. Step 2: Give the symbolic form that must be true when the original claim is false. If the original claim of p 7 0.5 is false, then p … 0.5 must be true. Step 3: This step is in two parts: Identify the alternative hypothesis H1 and identify the null hypothesis H0. ■ Identify H1: Using the two symbolic expressions p 7 0.5 and p … 0.5, the alternative hypothesis H1 is the one that does not contain equality. Of those two expressions, p 7 0.5 does not contain equality, so we get H1: p 7 0.5 continued
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