376 CHAPTER 8 Hypothesis Testing 8. Restate Decision in Nontechnical Terms Construct a confidence interval with a confidence level selected as in Table 8-1. Because a confidence interval estimate of a population parameter contains the likely values of that parameter, reject a claim that the population parameter has a value that is not included in the confidence interval. Table 8-1 Significance 0.01 Level for 0.05 Hypothesis 0.10 Test Two-Tailed Test One-Tailed Test 99% 95% 90% 98% 90% 80% Confidence Level for Confidence Interval Confidence Interval Method Restate this previous decision in simple nontechnical terms, and address the original claim. 5. Identify the Test Statistic Identify the test statistic that is relevant to the test and determine its sampling distribution (such as normal, t, chi-square). 4. Select Significance Level Select the significance level A based on the seriousness of a type I error. Make A small if the consequences of rejecting a true H0 are severe. • The values of 0.05 and 0.01 are very common. 2. Give Symbolic Form Give the symbolic form that must be true when the original claim is false. 1. Identify the Claim Identify the claim to be tested and express it in symbolic form. 3. Identify Null and Alternative Hypothesis Consider the two symbolic expressions obtained so far: • Alternative hypothesis H1 is the one NOT containing equality, so H1 uses the symbol . or , or Þ. • Null hypothesis H0 is the symbolic expression that the parameter equals the fixed value being considered. 7. Make a Decision • Reject H0 if P-value # a. • Fail to reject H0 if P-value . a. 6. Find Values Find the value of the test statistic and the P-value (see Figure 8-3). Draw a graph and show the test statistic and P-value. 7. Make a Decision • Reject H0 if the test statistic is in the critical region. • Fail to reject H0 if the test statistic is not in the critical region. 6. Find Values P-Value Method Critical Value Method Find the value of the test statistic and the critical values. Draw a graph showing the test statistic, critical value(s) and critical region. FIGURE 8-1 Procedure for Hypothesis Tests
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