Formulating the Hypothesis

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

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

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

4. Types of Statistical Errors • Type I Error - This type of statistical error occurs when the null hypothesis is true and is rejected. • 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 The critical value is Determined by the significance level. The cutoff value for a test statistic that leads to either rejecting or not rejecting the null hypothesis.

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

8. Establishing the Decision Rule(Figure 8-3) Sampling Distribution Maximum probability of committing a Type I error =  Do not reject H0 Reject H0

9. Establishing the Critical Value as a z -Value From the standard normal table Then Rejection region  = 0.10 0.5 0.4 0

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

11. Test Statistic in the Rejection Region Rejection region  = 0.10 0.5 0.4 0

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

13. Relationship Between the p-Value and the Rejection Region Rejection region  = 0.10 p-value = 0.0036 0.5 0.4 0

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

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

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