8-1 Basics of Hypothesis Testing 375 The Big Picture In the Chapter Problem, we have survey results showing that 52% of 926 Internet users utilize two-factor authentication to protect their online data. In Example 1, we have the claim that the population proportion p is such that p 7 0.5. Among 926 consumers, how many do we need to get a significantly high number who utilize two-factor authentication? ■ Clearly Not Significantly High: A result of 464 (or 50.1%) among 926 is just barely more than half, so 464 is clearly not significantly high. ■ Clearly Significantly High: A result of 925 (or 99.9%) among 926 is clearly significantly high. ■ Unclear: But what about a result such as 510 (or 55.1%) among 926? The formal method of hypothesis testing allows us to determine whether such a result is significantly high. Using Technology It is easy to obtain hypothesis-testing results using technology. The accompanying screen displays show results from four different technologies, so we can use computers or calculators to do all of the computational heavy lifting. Examining the four screen displays, we see some common elements. They all display a “test statistic” of z = 1.25 (rounded), and they all include a “P-value” of 0.1059 or 0.106 (rounded). These two results of the test statistic and P-value are important, but understanding the hypothesis-testing procedure is far more important. Focus on understanding how the hypothesis-testing procedure works and learn the associated terminology. Only then will results from technology make sense. CP Statdisk Minitab StatCrunch TI-83, 84 Plus Significance Hypothesis tests are also called tests of significance. In Section 4-1 we used probabilities to determine when sample results are significantly low or significantly high. This chapter formalizes those concepts in a unified procedure that is used often throughout many different fields of application. Figure 8-1 on the next page summarizes the procedures used in two slightly different methods for conducting a formal hypothesis test. We will proceed to conduct a formal test of the claim from Example 1 that p 7 0.5. In testing that claim, we will use the sample data from the survey cited in the Chapter Problem, with n = 926 and pn = 0.52.
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