1. Business Statistics - QBM117 Testing hypotheses about a population proportion

2. Objectives w To test a hypothesis about a population proportion w To practice hypothesis testing with further examples.

3. proportion Does the question ask us to test a hypothesis about a mean or a proportion? Testing a hypothesis about the population proportion, p Exercise 10.48 p357 (9.48 9323 abridged)

4. Step 1 Step 2 Step 3

5. 0 Critical value  = 0.05 Region of non-rejection 0.95 1.645 z

6. Step 1 Step 2 Step 3 Step 4

7. Step 5

8. 0  = 0.05 Region of non-rejection 0.95 1.645 z 1.4

9. Since 1.4 < 1.645 we do not reject H 0. Step 5 Step 6 There is insufficient evidence at  = 0.05 to conclude that the proportion is greater than 0.5.

10. proportion Does the question ask us to test a hypothesis about a mean or a proportion? Exercise 10.70 p360 (9.70 p326 abridged)

11. Step 1 Step 2 Step 3

12. 0 Critical value  = 0.05 Region of non-rejection 0.95 1.645 z

13. Step 1 Step 2 Step 3 Step 4

14. Step 5

15. 0  = 0.05 Region of non-rejection 0.95 1.645 z 2.9

16. Since 2.9 > 1.645 we reject H 0. Step 5 Step 6 There is sufficient evidence at  = 0.05 to conclude that the the campaign was a success.

17. Do we know the population standard deviation,  or do we only have the sample standard deviation s? mean Does the question ask us to test a hypothesis about a mean or a proportion?  Exercise 10.64 p360 (9.64 326 abridged)

18. Step 1 Step 2 Step 3

19. 0 Critical value  = 0.05 Region of non-rejection 0.95 z -1.645

20. Step 1 Step 2 Step 3 Step 4

21. Step 5

22. 0  = 0.05 Region of non-rejection 0.95 z -1.645 -1.68

23. Since -1.68 < -1.645 we reject H 0. Step 5 Step 6 There is sufficient evidence at  = 0.05 to conclude that the managers belief is correct.

24. Reading for next lecture Read Chapter 10 Sections 10.4 (Chapter 9 Section 9.4 abridged) Exercises to be completed before next lecture S&S 10.52 (9.52 abridged)