Aim: What is the P-value method for hypothesis testing? Quiz Friday P-value • Usually test hypotheses at the common alpha levels of 0.05 and 0.01 and sometimes 0.10 • The choice of the alpha level depends on the seriousness of the type I error • P-value (probability value): is the probability of getting a sample statistic (such as the mean) or a more extreme sample statistic in the direction of the alternative hypothesis when the null hypothesis is true – In other words, the P-value is the actual area under the standard normal distribution curve representing the probability of a particular sample statistic or a more extreme sample statistic occurring if the null hypothesis is true. Procedure 1. 2. 3. 4. 5. State the hypothesis and identity the claims Compute the test value Find the P-value Make the decision Summarize the results Example • A researcher wishes to test the claim that the average age of lifeguards in Ocean City is greater than 24 years. She selects a sample of 36 guards and find the mean of the sample to be 24.7 years, with a standard deviation of 2 years. Is there evidence to support the claim at α = 0.05? Use the P-value method. Example Solution • Step 1: State the hypotheses and identify the claim H 0 : 24 H1 : 24 • Step 2: Compute the test value Z 24.7 24 2.10 2 36 • Step 3: Find the P-value (from z-table) – area under the curve .5000 .4821 .0179 • Step 4: Make the decision – Since the P-value is less than 0.05, the decision is to rejected the null hypothesis • Step 5: Summarize Results – There is enough evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years. Decision Rule When using a P-value • If the P-value ≤ α, reject the null hypothesis • If the P-value is > α, do not reject the null hypothesis

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