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Business Statistics - QBM117

Business Statistics - QBM117. Testing hypotheses about a population proportion. Objectives. To test a hypothesis about a population proportion To practice hypothesis testing with further examples. Testing a hypothesis about the population proportion, p.

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Business Statistics - QBM117

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

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

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

  4. Step 1 Step 2 Step 3

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

  6. Step 1 Step 2 Step 3 Step 4

  7. Step 5

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

  9. Step 5 Step 6 Since 1.4 < 1.645 we do not reject H0. There is insufficient evidence at  = 0.05 to conclude that the proportion is greater than 0.5.

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

  11. Step 1 Step 2 Step 3

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

  13. Step 1 Step 2 Step 3 Step 4

  14. Step 5

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

  16. Step 5 Step 6 Since 2.9 > 1.645 we reject H0. There is sufficient evidence at  = 0.05 to conclude that the the campaign was a success.

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

  18. Step 1 Step 2 Step 3

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

  20. Step 1 Step 2 Step 3 Step 4

  21. Step 5

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

  23. Step 5 Step 6 Since -1.68 < -1.645 we reject H0. 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)

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