1. Sta220 - Statistics Mr. Smith Room 310 Class #19

2. Section 6-3 and 6-4 Notes

3. 6-3: Test of Hypothesis about a Population Mean: Normal (z) Statistic

4. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

5. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

6. Example 6.3.1. The effect of drugs and alcohol on the nervous system has been the subject of considerable research. Suppose a research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each rat to a neurological stimulus, and recording its response time. The neurologist knows that the mean response time for rats not injected with the drug (the “control” mean) is 1.2 seconds. She wishes to test whether the mean response time for drug-injected rats differs from 1.2 seconds. At α =.01, conduct the test of hypothesis.

7. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

8. Solution

9. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Two-tailed rejection region:  =.01

10. Solution:

11. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

12. Example 6.3.2.

14. Solution

15. 6.4: Observed Significance Levels: p-Values

17. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

18. Recall from Section 6.1

20. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an upper-tailed test when z = 2.12

21. The area A in the previous figure is given in Table III as.4830. Therefore, the upper-tail area corresponding to z = 2.12 is p-value =.5 -.4830 =.0170

23. Note:

24. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

25. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an one-tailed test

26. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Finding the p-value for an two-tailed test; p- value = 2(p/2)

27. Go back to Example 6.3.1.

28. The observed value of the test statistic was z = -3.0. p-value = P(z +3.0) = P(|z|> 3.0) P(z < -3.0) =.5 -.4987 =.0013 Since this is a two tail test, we must double the area. 2P(z < - 3.0) = 2(.0013) =.0026

29. Example 6.4.1

30. Copyright © 2013 Pearson Education, Inc.. All rights reserved.

31. Solution

33. Example 6.4.2

34. Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure