1. Chapter 8 Hypothesis Testing

2. Section 8-1: Steps in Hypothesis Testing – Traditional Method Learning targets – IWBAT understand the definitions used in hypothesis testing. – IWBAT state the null and alternative hypotheses. – IWBAT find critical values for the z-test

3. Vocabulary Statistical hypothesis – a conjecture about a population parameter. This conjecture may or may not be true. Null hypothesis – symbolized as H 0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. Alternative hypothesis – symbolized as H 1, is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.

9. Practice Problems

10. Solutions

11. A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected. The numerical value obtained from a statistical test is called the test value.

12. Errors In hypothesis testing there are 2 types of errors: -Type I Error – you reject the null hypothesis when it is true -Type II Error – you do not reject the null hypothesis when it is false Example: jury trial outcomes

13. Level of Significance represented by alpha (α) the value used to determine the critical value that helps determine whether or not to reject the null hypothesis Also referred to as the P-value which is the area under the curve

14. Critical Value and Region Critical value – the z-value that separates the critical region from the noncritical region (symbol C.V.) Critical/rejection region – range of values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected Noncritical/nonrejection region – range of values of the test value that indicates that the difference was probably due to chance and the null hypothesis should not be rejected

15. One-Tailed Test

16. Two-Tailed Test

17. %Left-tailedRight-tailedTwo-tailed.2080-.84.841.28.1585-1.031.031.44.1090-1.281.281.645.0595-1.6451.6451.96.0298-2.052.052.33.0199-2.332.332.575 This chart contains the z-scores for the most used α The z-scores are found the same way they were in Section 6-1.

18. Practice Problems

20. Section 8-2 Z Test for a Mean

21. Steps 1.State null and alternative hypotheses. 2.Find the critical values 3.Compute the test value 4.Make decision to reject or accept 5.Summarize the results

22. Critical Value and Region Critical value – the z-value that separates the critical region from the noncritical region (symbol C.V.) Critical/rejection region – range of values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected Noncritical/nonrejection region – range of values of the test value that indicates that the difference was probably due to chance and the null hypothesis should not be rejected

23. %Left-tailedRight-tailedTwo-tailed.2080-.84.841.28.1585-1.031.031.44.1090-1.281.281.645.0595-1.6451.6451.96.0298-2.052.052.33.0199-2.332.332.575 This chart contains the z-scores for the most used α The z-scores are found the same way they were in Section 6-1.

24. Formula

26. One-Tailed Test

27. Two-Tailed Test

28. Summarize Results To summarize the results you need to state whether there is or is not sufficient evidence to support the claim (the alternative hypothesis) - If we reject the null there is sufficient evidence to support the claim - If we fail to reject the null there is not sufficient evidence to support the claim. Example: There is sufficient evidence to support the claim that students will have an average score of 19 on the ACT.

32. Two-tailed with α=.05, therefore critical region starts at 1.96. Since the situation is two tailed, we have a tail to the right and a tail to the left. If we compare the two z-scores, we notice that the test statistic is greater than the critical value. Therefore, our decision is to reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the valve does not perform to specifications.

33. Since the claim is “less than” the situation is one-tailed. The z-score critical value for α=.01 is -2.33 When we compare the two z-scores, we notice that the test statistic is less than the critical value and falls in the rejection region. Therefore, we will reject the null hypothesis. Since we have rejected the null, we can conclude there is sufficient evidence to support the claim that the state employees earn on average less than the federal employees.