Textbook Question
Explain the procedure for testing a hypothesis using the P-value Approach. What is the criterion for judging whether to reject the null hypothesis?
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:46 minutesProblem 10.R.21
Textbook Question
Explain the procedure for testing a hypothesis using the Classical Approach. What is the criterion for judging whether to reject the null hypothesis?
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Step 1: Formulate the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). The null hypothesis usually represents the status quo or no effect, while the alternative represents the claim you want to test.
Step 2: Choose a significance level (\(\alpha\)), which is the probability of rejecting the null hypothesis when it is actually true (Type I error). Common values are 0.05, 0.01, or 0.10.
Step 3: Determine the appropriate test statistic based on the sample data and the type of test (e.g., \(z\)-test, \(t\)-test). Calculate the value of this test statistic from your sample.
Step 4: Find the critical value(s) from the theoretical distribution corresponding to the chosen significance level \(\alpha\). These critical values define the rejection region(s) for the test statistic.
Step 5: Compare the calculated test statistic to the critical value(s). If the test statistic falls into the rejection region, reject the null hypothesis; otherwise, do not reject it. This comparison is the criterion for deciding whether to reject \(H_0\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null and Alternative Hypotheses
The null hypothesis (H0) represents the default assumption or status quo, while the alternative hypothesis (H1) reflects the claim being tested. Hypothesis testing involves evaluating evidence against H0 to determine if it should be rejected in favor of H1.
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Step 1: Write Hypotheses
Classical Approach to Hypothesis Testing
The Classical Approach involves defining a significance level (α), determining the critical region based on the sampling distribution, and comparing the test statistic to critical values. If the test statistic falls in the critical region, H0 is rejected; otherwise, it is not rejected.
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Rejection Criterion and Significance Level
The criterion for rejecting H0 is whether the test statistic lies within the critical region determined by the significance level α, which represents the probability of a Type I error. If the observed value is extreme enough (beyond critical values), H0 is rejected.
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