HYPOTHESIS TESTING

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HYPOTHESIS TESTING

• CHAPTER 5
• BCT 2053

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CONTENT

• 5.1 The Hypothesis Testing Procedure in General
• 5.2 Hypothesis Testing for Mean with known and
• unknown Variance
• 5.3 Hypothesis Testing for Different Mean with
• known and unknown Variance
• 5.4 Hypothesis Testing for Proportion
• 5.5 Hypothesis Testing for Variance
• 5.6 The Chi-Square Independence Test

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OBJECTIVES

• After completing this chapter, you should be able
  to
• 1. Understand the Definitions used in Hypothesis
  
• Testing
• 2. State the Null and Alternative Hypothesis
• 3. Test the hypothesis of Population Means for
  Large
• and Small Samples
• 4. Test the hypothesis of Proportions
• 5. Test the hypothesis of Variance
• 6. Test the hypothesis of Independent Event

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5.1 The Hypothesis Testing Procedure in General

• Hypothesis
• A statement that something TRUE
• Null hypothesis (Ho)
• A hypothesis to be tested
• Alternative Hypothesis (H1)
• A hypothesis to be considered as an alternative
  to the null hypothesis

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How to make Null hypothesis

• Should have an equal sign
• Generally,

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How to make Alternative hypothesis

• Should reflect the purpose of the hypothesis test
  and different from the null hypothesis
• Generally (3 types)

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Basic logic of Hypothesis Testing

• Accept null hypothesis
• if the sample data are consistent with the null
  hypothesis
• Reject null hypothesis
• if the sample data are inconsistent with the null
  hypothesis, so accept Alternative hypothesis
• Test statistics
• the statistics used as a basis for deciding
  whether the null hypothesis should be rejected
  (z, t, Khi, F)

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Basic logic of Hypothesis Testing

• Rejection (Critical) Region
• the set of values for the test statistics that
  leads to rejection of the null hypothesis
• Nonrejection (NonCritical) Region
• the set of values for the test statistics that
  leads to nonrejection of the null hypothesis
• Critical values
• the values of the test statistics that separate
  the rejection and nonrejection regions. A
  critical value is considered part of the
  rejection region

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Rejection Region
Accept Ho
Accept Ho
Accept Ho
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Type I and II Error

• Type I Error
• - Rejecting the null hypothesis when it is in
  fact true

• Type II Error
• -Not rejecting the null hypothesis when it is in
  fact false

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Hypothesis Testing Common Phrase
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Example

• State the null and alternative hypotheses for
  each conjecture.
• A researcher thinks that if expectant mothers use
  vitamin pills, the birth weight of the babies
  will increase. The average birth weight of the
  population is 8.6 pounds.
• An engineer hypothesizes that the mean number of
  defects can be decreased in a manufacturing
  process of compact disks by using robots instead
  of humans for certain tasks. The mean number of
  defective disks per 1000 is 18.
• A psychologist feels that playing soft music
  during a test will change the results of the
  test. The psychologist is not sure whether the
  grades will be higher or lower. In the past, the
  mean of the scores was 73.

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Steps In Hypothesis Testing

• Define the parameter used
• Define the null and alternative hypothesis
• Define all the given information
• Chose appropriate Test Statistics
• Find Critical value
• Test the hypothesis
• Make conclusion

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5.2 Hypothesis Testing for Mean with
known and unknown Variance
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5.3 Hypothesis Testing for Different Mean with
known and unknown Variance
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5.4 Hypothesis testing for proportion p
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5.5 Hypothesis Testing for Variance
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5.6 The Chi-Square Independence Test

• To test the independence of two tests
• H0 The tests are independent
• (x has no relationship with y)
• H1 The tests are not independent
• (x has relationship with y)
• Reject H0 if
• where and

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Example 1
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Example 2
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Example 3

• A sociologist wishes to see whether the number of
  years of college a person has completed is
  related to his or her place of residence. A
  sample of 88 people is selected and classified as
  shown. At 0.05 significance level, can the
  sociologist conclude that the years of college
  education are dependent on the persons location?

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Summary

• A hypothesis test produces a number between 0 and
  1 that measure the degree of certainty we may
  have in the truth of a hypothesis about a
  quantity such as population mean or proportion
• Hypothesis test are closely related to confidence
  interval. Whenever a confidence interval can be
  computed, a hypothesis test can also be
  performed, and vice versa.
• The End

Thank You