Procedure for Hypothesis Tests 8. Restate Decision in Nontechnical Terms 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. Finding P-Values Is the test statistic to the right or left of center? Left Right Two-tailed Left-tailed Right-tailed P-value 5 twice the area to the left of the test statistic P-value 5 area to the left of the test statistic P-value 5 twice the area to the right of the test statistic P-value 5 area to the right of the test statistic What type of test? Start Start No No Yes Yes Reject H0 Fail to reject H0 Wording of Final Conclusion “There is sufficient evidence to support the claim that... (original claim).” “There is not sufficient evidence to support the claim that... (original claim).” Original claim does not contain equality and becomes H1 Original claim contains equality Does the original claim contain the condition or equality? Do you reject H0? No Yes Reject H0 Fail to reject H0 “There is sufficient evidence to warrant rejection of the claim that... (original claim).” (This is the only case in which the original claim is supported.) (This is the only case in which the original claim is rejected.) “There is not sufficient evidence to warrant rejection of the claim that... (original claim).” Do you reject H0? Hypothesis Tests: Wording of Final Conclusion 748
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