374 CHAPTER 8 Hypothesis Testing The “property of a population” referred to in the preceding definitions is often the value of a population parameter, so here are some examples of typical hypotheses (or claims): ■ p 7 0.5 “Most Internet users (more than half) utilize two-factor authentication to protect their online data.” ■ m 6 98.6°F “The mean body temperature of humans is less than 98.6°F.” ■ s = 15 “The population of college students has IQ scores with a standard deviation equal to 15.” 8-5 Resampling: Using Technology for Hypothesis Testing • Use the resampling methods of bootstrapping and randomization to test a claim about a population proportion, population mean, and population standard deviation or variance. DEFINITIONS In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a procedure for testing a claim about a property of a population. PART 1 Basic Concepts of Hypothesis Testing We begin with two very basic definitions. Consider the claim from the Chapter Problem that “most Internet users utilize twofactor authentication to protect their online data.” Using p to denote the proportion of Internet users who utilize two-factor authentication, the claim that “most” Internet users (or the “majority”) is equivalent to the claim that the proportion is greater than half, or p 7 0.5. The expression p 7 0.5 is the symbolic form of the original claim. CP EXAMPLE 1 Most Internet Users Utilize Two-Factor Authentication to Protect Their Online Data Key Concept In this section we present key components of a formal hypothesis test. The concepts in this section are general and apply to hypothesis tests involving proportions, means, or standard deviations or variances. In Part 1, we begin with the “big picture” to understand the basic underlying approach to hypothesis tests. Then we describe null and alternative hypotheses, significance level, types of tests (two-tailed, left-tailed, right-tailed), test statistic, P-value, critical values, and statements of conclusions. In Part 2 we describe types of errors (type I and type II). In Part 3 we describe the power of a hypothesis test. 8-1 Basics of Hypothesis Testing
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