sbe10_06a-51 - Statistics for Business and Economics...

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Statistics for Business and Economics Chapter 6 Inferences Based on a Single Sample: Tests of Hypothesis
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Learning Objectives 1. Distinguish Types of Hypotheses 2. Describe Hypothesis Testing Process 3. Explain p-Value Concept 4. Solve Hypothesis Testing Problems Based on a Single Sample 5. Explain Power of a Test
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Statistical Methods Statistical Methods Estimation Hypothesis Testing Inferential Statistics Descriptive Statistics
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Nonstatistical Hypothesis Testing A criminal trial is an example of hypothesis testing without the statistics. In a trial a jury must decide between two hypotheses. The null hypothesis is H 0 : The defendant is innocent The alternative hypothesis or research hypothesis is H 1 : The defendant is guilty The jury does not know which hypothesis is true. They must make a decision on the basis of evidence presented.
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Nonstatistical Hypothesis Testing In the language of statistics convicting the defendant is called rejecting the null hypothesis in favor of the alternative hypothesis . That is, the jury is saying that there is enough evidence to conclude that the defendant is guilty (i.e., there is enough evidence to support the alternative hypothesis).
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Nonstatistical Hypothesis Testing If the jury acquits it is stating that there is not enough evidence to support the alternative hypothesis . Notice that the jury is not saying that the defendant is innocent, only that there is not enough evidence to support the alternative hypothesis. That is why we never say that we accept the null hypothesis.
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Nonstatistical Hypothesis Testing There are two possible errors. A Type I error occurs when we reject a true null hypothesis. That is, a Type I error occurs when the jury convicts an innocent person. A Type II error occurs when we don’t reject a false null hypothesis. That occurs when a guilty defendant is acquitted.
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Nonstatistical Hypothesis Testing The probability of a Type I error is denoted as α (Greek letter alpha ). The probability of a type II error is β (Greek letter beta ). The two probabilities are inversely related. Decreasing one increases the other.
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Nonstatistical Hypothesis Testing 5. Two possible errors can be made. Type I error: Reject a true null hypothesis Type II error: Do not reject a false null hypothesis. P(Type I error) = α P(Type II error) = β
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Decision Results H 0 : Innocent Jury Trial Actual Situation Verdict Innocent Guilty Innocent Correct Error Guilty Error Correct H 0 Test Actual Situation Decision H 0 True H 0 False Accept H 0 1 – Type II Error ( ) Reject H 0 Type I Error ( ) Power (1 – )
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& Have an Inverse Relationship You can’t reduce both errors simultaneously!
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Nonstatistical Hypothesis Testing In our judicial system Type I errors are regarded as more serious. We try to avoid convicting innocent people. We are more willing to acquit guilty people.
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