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Business Statistics - QBM117 Testing hypotheses about a population proportion

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

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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)

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Step 1 Step 2 Step 3

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

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Step 1 Step 2 Step 3 Step 4

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Step 5

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

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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.

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

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Step 1 Step 2 Step 3

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

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Step 1 Step 2 Step 3 Step 4

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Step 5

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

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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.

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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)

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Step 1 Step 2 Step 3

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

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Step 1 Step 2 Step 3 Step 4

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Step 5

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

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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.

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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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