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CHAPTER 9 HYPOTHESIS TESTING: CLASSICAL TECHNIQUES

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Null Hypothesis - a description of what people have long believed to be true ... Confidence Level of the Hypothesis Test - the probability of accepting the null ... – PowerPoint PPT presentation

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Title: CHAPTER 9 HYPOTHESIS TESTING: CLASSICAL TECHNIQUES


1
CHAPTER 9HYPOTHESIS TESTING CLASSICAL
TECHNIQUES
2
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.

3
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)

4
  • C. Exact Hypothesis - a null hypothesis that
    specifies a single value for the unknown parameter

5
  • D. Inexact Hypothesis - an alternative hypothesis
    that specifies a range of values for the unknown
    parameter

6
  • E. Two-sided Hypothesis - an alternative
    hypothesis that holds for deviations from the
    null hypothesis in either direction

7
  • F. One-sided Hypothesis - an alternative
    hypothesis that holds for deviations from the
    null hypothesis in one direction only

8
  • 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

9
Statistics Commonly Used for Tests About a
Population Mean
10
Statistics Commonly Used for Tests About a
Population Mean
11
  • 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

12
  • B. Acceptance Region numerical values of the
    test statistic for which the null hypothesis is
    accepted lie here

13
  • C. Rejection Region - numerical values of the
    test statistic for which the null hypothesis is
    rejected lie here

14
  • 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

15
  • 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)

16
  • G. Critical Value (cutoff point or acceptance
    number) - value of a test statistic that divides
    all possible values into an acceptance and
    rejection region

17
  • H. Two-tailed Test - when the alternative
    hypothesis is two-sided

18
  • I. One-tailed Test - when the alternative
    hypothesis is one-sided

19
  • J. Lower-tailed Test - entire rejection region is
    in the lower tail

20
  • K. Upper-tailed Test - entire rejection region is
    in the upper tail

21
  • 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

22
  • 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

23
TABLE 9.3 Evaluating the Outcome of a
Hypothesis Test
24
FIGURE 9.3 - The Trade-Off Between Type I and
Type II Error
25
CAUTION
26
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

31
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