1. Formulating the Hypothesis null hypothesis 4 The null hypothesis is a statement about the population value that will be tested. null hypothesis 4 The null hypothesis will be rejected only if the sample data provide substantial contradictory evidence.

2. Formulating the Hypothesis alternativehypothesis 4 The alternative hypothesis is the hypothesis that includes all population values not covered by the null hypothesis. alternative hypothesis 4 The alternative hypothesis is deemed to be true if the null hypothesis is rejected.

3. Formulating the Hypothesis research hypothesis alternativehypothesis The research hypothesis (usually the alternative hypothesis ): 4 Decision maker attempts to demonstrate it to be true. 4 Deemed to be the most important to the decision maker. 4 Not declared true unless the sample data strongly indicates that it is true.

4. Types of Statistical Errors 4 Type I Error 4 Type I Error - This type of statistical error occurs when the null hypothesis is true and is rejected. 4 Type II Error 4 Type II Error - This type of statistical error occurs when the null hypothesis is false and is not rejected.

5. Types of Statistical Errors

6. Establishing the Decision Rule critical value The critical value is 4 Determined by the significance level. 4 The cutoff value for a test statistic that leads to either rejecting or not rejecting the null hypothesis.

7. Establishing the Decision Rule significance level The significance level is the maximum probability of committing a Type I statistical error. The probability is denoted by the symbol .

8. Reject H 0 Do not reject H 0 Sampling Distribution Maximum probability of committing a Type I error =  Establishing the Decision Rule (Figure 8-3)

9. Rejection region  = 0.10 0 From the standard normal table Then 0.50.4 Establishing the Critical Value as a z -Value

10. Establishing the Decision Rule test statistic The test statistic is a function of the sampled observations that provides a basis for testing a statistical hypothesis.

11. Rejection region  = 0.10 0 0.50.4 Test Statistic in the Rejection Region

12. Establishing the Decision Rule p-value The p-value is 4 The probability of obtaining a test statistic at least as extreme as the test statistic we calculated from the sample. 4 Also known as the observed significance level.

13. Rejection region  = 0.10 0 0.50.4 Relationship Between the p- Value and the Rejection Region p-value = 0.0036

14. Using the p-Value to Conduct the Hypothesis Test p-value is less than or equal to a 4If the p-value is less than or equal to a, reject the null hypothesis. p-value is greater than a 4If the p-value is greater than a, do not reject the null hypothesis. Example: For  = 0.05 with the p-value = 0.02 for a particular test, then the null hypothesis is rejected.

15. One-Tailed Hypothesis Tests one-tailed hypothesis test A one-tailed hypothesis test is a test in which the entire rejection region is located in one tail of the test statistic’s distribution.

16. Two-Tailed Hypothesis Tests two-tailed hypothesis test A two-tailed hypothesis test is a test in which the rejection region is split between the two tails of the test statistic’s distribution.

17. 0 Two-Tailed Hypothesis Tests (Figure 8-7)

18. When  Is Unknown 4The sample standard deviation is used. 4The test statistic is calculated as 4The critical value is found from the t-table (Appendix F) using n-1 degrees of freedom.