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How much evidence is there that H0: μ = 80 is false and Ha: μ > 80 is true? Exercises for Section 9.2 CONCEPTS 9.14 Explain what a critical value is, and explain how it is used to test a hypothesis. 9.15 Explain what a p-value is, and explain how it is used to test […]

Explain what a p-value is, and explain how it is used to test a hypothesis. Exercises for Section 9.2 CONCEPTS 9.14 Explain what a critical value is, and explain how it is used to test a hypothesis. 9.15 Explain what a p-value is, and explain how it is used to test a hypothesis. METHODS AND

Explain what a critical value is, and explain how it is used to test a hypothesis. Exercises for Section 9.2 CONCEPTS 9.14 Explain what a critical value is, and explain how it is used to test a hypothesis. 9.15 Explain what a p-value is, and explain how it is used to test a hypothesis. METHODS

Interpreting the Weight of Evidence against the Null Hypothesis If the p-value for testing H0 is less than • .10, we have some evidence that H0 is false. • .05, we have strong evidence that H0 is false. • .01, we have very strong evidence that H0 is false. • .001, we have extremely strong

Measuring the weight of evidence against the null hypothesis We have seen that in some situations the decision to take an action is based solely on whether a null hypothesis can be rejected in favor of an alternative hypothesis by setting α equal to a single, prespecified value. For example, in the trash bag case

Using confidence intervals to test hypotheses Confidence intervals can be used to test hypotheses. Specifically, it can be proven that we can reject H0: μ = μ0 in favor of Ha: μ ≠ μ0 by setting the probability of a Type I error equal to α if and only if the 100(1 − α) percent confidence interval

Define the test statistic and assume that the population sampled is normally distributed, or that the sample size n is large. We can test H0: μ = μ0 versus a particular alternative hypothesis at level of significance α by using the appropriate critical value rule, or, equivalently, the corresponding p-value. Place Your Order Here!

Using a critical value rule: 4 Determine the critical value rule for deciding whether to reject H0. Use the specified value of α to find the critical value in the critical value rule. 5 Collect the sample data and compute the value of the test statistic. 6 Decide whether to reject H0 by using the

A summary of the seven steps of hypothesis testing For almost every hypothesis test discussed in this book, statisticians have developed both a critical value rule and a p-value that can be used to perform the hypothesis test. Furthermore, it can be shown that for each hypothesis test the p-value has been defined so that

Comparing the critical value and p-value methods Thus far we have considered two methods for testing H0: μ = 50 versus Ha: μ > 50 at the .05 and .01 values of α. Using the first method, we determine if the test statistic value z = 2.20 is greater than the critical values z.05 =