# Lesson 05 chapter 8 hypothesis testing

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### Transcript of Lesson 05 chapter 8 hypothesis testing

Inductive StatisticsDr. Ning DINGn.ding@pl.hanze.nl

I.007 IBS, Hanze

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Table of ContentsReview:Chapter 5 Probability DistributionChapter 6 Sampling DistributionChapter 7 Estimation

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 5: Probability DistributionNormal Distributioncontinuousz=1.00P=0.3413Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 5: Probability DistributionNormal Distributioncontinuousz=1.00P=0.6826Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 6 Sampling Distribution

Infinitepopulation Finite populationReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 7 EstimationInterval Estimates of the MeanInterval Estimates of the Proportion

is known: is unknown:

n

Chapter 8 Testing Hypotheses-Summary

Ch 8 Example P.417H0H1There is no difference between the sample mean and the hypothesized population mean. There is a difference between the sample mean and the hypothesized population mean. H0 : = 10H1 : > 15H1 : < 2H1 : 15For example:MeanReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses: Practice8-28Step 1: List the known variablesStep 2: Formulate HypothesesStep 3: Calculate the standard errorStep 5: Calculate the z value

0.05P=0.45z=-1.645

Step 4: Visualize the confidence levelWith acceptance region accept H0so, new bulb producing is good!Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Ch 8 No. Example P.433Example:Step 1: List the known variablesStep 2: Formulate HypothesesStep 3: Calculate the standard errorThe HR director thinks that the average aptitude test is 90. The manager sampled 20 tests and found the mean score is 80 with standard deviation 11.

If he wants to test the hypothesis at the 0.10 level of significance, what is the procedure?Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Ch 8 No. Example P.433Example:Step 4: Visualize the confidence levelStep 5: Calcuate the t valueThe HR director thinks that the average aptitude test is 90. The manager sampled 20 tests and found the mean score is 80 with standard deviation 11.

If he wants to test the hypothesis at the 0.10 level of significance, what is the procedure?Appendix Table 2

t=-1.729 +1.729Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Ch 8 No. Example P.433Step 4: Visualize the confidence levelAppendix Table 2

Confidence Intervaldf

12 0.05 0.10

1.782Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses-Summary

Ch 8 Example P.417H0H1There is no difference between the sample mean and the hypothesized population mean. There is a difference between the sample mean and the hypothesized population mean. H0 : = 10H1 : > 15H1 : < 2H1 : 15For example:MeanProportionReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses:Proportion

Ch 8 Example P.427HR director tell the CEO that the promotability of the employees is 80%. The president sampled 150 employees and found that 70% are promotable.

The CEO wants to test at the 0.05 significance level the hypothesis that 0.8 of the employees are promotable. Example:Step 1: List the known variablesStep 2: Formulate HypothesesStep 3: Calculate the standard errorProportionReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses:Proportion

Ch 8 Example P.427HR director tell the CEO that the promotability of the employees is 80%. The president sampled 150 employees and found that 70% are promotable.

The CEO wants to test at the 0.05 significance level the hypothesis that 0.8 of the employees are promotable. Example:Step 4: Visualize the confidence levelStep 5: Calculate the z score

ProportionReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses:Practice

Ch 8 SC 8-9 P.431. Step 4: Visualize the confidence levelStep 5: Calculate the z scoreStep 1: List the known variablesStep 2: Formulate HypothesesStep 3: Calculate the standard errorSC 8-9Proportion

Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 8 Testing Hypotheses: Measuring Power of a Hypothesis Test

TrueNot TrueAcceptRejectH0Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Test Hypotheses for the MeanTest Hypotheses for the Proportion

is known is unknown

n

Chapter 8 Testing Hypotheses--Summary

H0: =XXH1 : > XXH1 : < XXH1 : XX=0.05 z: P=0.45 z= +1.645t: =0.10

=0.05 z: P=0.475 z= 1.96t: =0.10

=0.05 z: P=0.45 z= -1.645t: =0.10

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Chapter 9 Testing Hypotheses: Two-Sample Tests

Lets compare !Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Basics

Independent SamplesDependent SamplesReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Basics-Independent

is known: is unknown:

H0H1

n

Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples

9.1.1 Difference between means: Large SamplesExample:Ch 9 Example P.456Whether the hourly wages of semiskilled workers are the same between females and males. The survey showed:Step 1: Formulate hypotheses

Two-tailed TestStep 2: Find the Estimated Standard Error of DifferenceEstimated Standard Error of DifferenceReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests : Two-Independent Samples

z=-1.96 +1.96Step 3: Visualize and find the z valuesStep 2: Find the Standard Error

Ch 9 Example P.456Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples

9.1.1 Difference between means: Large SamplesExample:Ch 9 Example P.456Whether the hourly wages of female semiskilled workers are lower than that of males. The survey showed:Step 1: Formulate hypotheses

One-tailed Test

P=0.45z=-1.645Step 2: Visualize and find the z values

Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice

Ch 9 No.9-2 P.460Step 1: Formulate hypotheses

9-2

P=0.48 z=Step 2: Find the Standard ErrorStep 3: Visualize and Calculate the z scores

- 2.05Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples

9.1.2 Difference between means: Small SamplesExample:Ch 9 Example P.462Which program is more effective in raising sensitivity? The survey showed:Step 1: Formulate hypotheses

One-tailed Test

Step 2: Find the Pooled Estimate of 2Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Two-Independent Samples

9.1.2 Difference between means: Small SamplesCh 9 Example P.462

t=1.708

Step 3: Calculate the standard error

Step 4: Visualize and find the t scores

df=(12-1)+(15-1)=25Areas in both tails combined=0.10Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Practice

Ch 9 No. 9-9 P.466Step 1: Formulate hypotheses

9-9

Step 2: Find the Pooled Estimate of 2Step 3: Calculate the standard errorStep 4: Visualize and Find the t scores

One-tailed Testdf = 16 area=0.10 t=1.746

Review:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples

9.2 Dependent SamplesReview:Chapter 5 Chapter 6 Chapter 7

Chapter 8 Testing Hypothesis~Test for Mean* when is known* when is unknown AND n=

Chapter 9 Testing Hypotheses: Two-Sample Tests: Dependent Samples

9.2 Dependent SamplesCh

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