CHAPTER 9 HYPOTHESIS TESTING: CLASSICAL TECHNIQUES

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CHAPTER 9HYPOTHESIS TESTING CLASSICAL
TECHNIQUES
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Introduction

• A. Hypothesis - a proposition (some belief about
  reality) tentatively advanced as possibly true
• B. Hypothesis Testing - a systematic approach to
  assessing tentative beliefs about reality it
  involves confronting those beliefs with evidence
  and deciding whether the beliefs can be
  maintained as reasonable or must be discarded as
  untenable.

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4 Major Steps

• Step 1 Formulating 2 Opposing Hypotheses

• A. Null Hypothesis - a description of what
  people have long believed to be true (status quo,
  conventional wisdom)

• B. Alternative Hypothesis - new claim that
  contradicts the null hypothesis (conventional
  wisdom)

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• C. Exact Hypothesis - a null hypothesis that
  specifies a single value for the unknown parameter

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• D. Inexact Hypothesis - an alternative hypothesis
  that specifies a range of values for the unknown
  parameter

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• E. Two-sided Hypothesis - an alternative
  hypothesis that holds for deviations from the
  null hypothesis in either direction

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• F. One-sided Hypothesis - an alternative
  hypothesis that holds for deviations from the
  null hypothesis in one direction only

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• Step 2 Selecting a Test Statistic

• Test Statistic a statistic computed from a
  simple random sample taken from the population of
  interest in a hypothesis test and then used for
  establishing the probable truth or falsity of the
  null hypothesis

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Statistics Commonly Used for Tests About a
Population Mean
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Statistics Commonly Used for Tests About a
Population Mean
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• Step 3 Deriving a Decision Rule

• A. Decision Rule - a hypothesis testing rule that
  specifies in advance, for all possible values of
  a test statistic that might be computed from a
  sample, whether the null hypothesis should be
  accepted or whether it should be rejected in
  favor of the alternative hypothesis

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• B. Acceptance Region numerical values of the
  test statistic for which the null hypothesis is
  accepted lie here

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• C. Rejection Region - numerical values of the
  test statistic for which the null hypothesis is
  rejected lie here

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• D. Statistically Significant - numerical values
  of the test statistic for which the null
  hypothesis is rejected are considered

• E. Not Statistically Significant - numerical
  values of the test statistic for which the null
  hypothesis is accepted are considered

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• F. Significance Level (size of a hypothesis test)
  - the (arbitrary) maximum proportion of all
  sample results that are possible that is
  considered sufficiently unusual to reject the
  null hypothesis when the null hypothesis is true
  (symbolized by alpha)

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• G. Critical Value (cutoff point or acceptance
  number) - value of a test statistic that divides
  all possible values into an acceptance and
  rejection region

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• H. Two-tailed Test - when the alternative
  hypothesis is two-sided

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• I. One-tailed Test - when the alternative
  hypothesis is one-sided

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• J. Lower-tailed Test - entire rejection region is
  in the lower tail

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• K. Upper-tailed Test - entire rejection region is
  in the upper tail

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• Step 4 Taking a Sample, Computing the Test
  Statistic, and Confronting It with the Decision
  Rule

• A. Type I Error (Error of Rejection) - the
  rejection of a true null hypothesis

• B. Alpha Risk - the probability of making a Type
  I Error

• C. Confidence Level of the Hypothesis Test - the
  probability of accepting the null hypothesis when
  the null hypothesis is true

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• D. Type II Error (Error of Acceptance) - the
  acceptance of a false null hypothesis

• E. Beta Risk - the probability of making a Type
  II Error

• F. Power of the Hypothesis Test - the probability
  of rejecting the null hypothesis when the null
  hypothesis is false

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TABLE 9.3 Evaluating the Outcome of a
Hypothesis Test
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FIGURE 9.3 - The Trade-Off Between Type I and
Type II Error
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CAUTION
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VI. Large-Sample Tests of a Population Mean

• A. 2-Tail Test

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• B. Lower-Tail Test

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• VII. Small-Sample Tests of a Population Mean

• A. Upper-Tail Test

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