Chapter_08 - Chapter 8: Inferences Based on a Single...

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Unformatted text preview: Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses Statistics McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 2 Where We’ve Been Calculated point estimators of population parameters Used the sampling distribution of a statistic to assess the reliability of an estimate through a confidence interval McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 3 Where We’re Going Test a specific value of a population parameter Measure the reliability of the test 8.1: The Elements of a Test of Hypotheses McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 4 Confidence Interval Where on the number line do the data point us? (No prior idea about the value of the parameter.) Hypothesis Test Do the data point us to this particular value? (We have a value in mind from the outset.) μ? μ? μ ? 8.1: The Elements of a Test of Hypotheses McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 5 Null Hypothesis : H •This will be supported unless the data provide evidence that it is false • The status quo Alternative Hypothesis : H a •This will be supported if the data provide sufficient evidence that it is true • The research hypothesis 8.1: The Elements of a Test of Hypotheses If the test statistic has a high probability when H is true, then H 0 is not rejected. If the test statistic has a (very) low probability when H is true, then H 0 is rejected. McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 6 8.1: The Elements of a Test of Hypotheses McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 7 8.1: The Elements of a Test of Hypotheses Reality ↓ / Test Result → Do not reject H Reject H H is true Correct! Type I Error: rejecting a true null hypothesis P(Type I error) = H is false Type II Error: not rejecting a false null hypothesis P(Type II error) = Correct! McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 8 8.1: The Elements of a Test of Hypotheses McClave, Statistics, 11th ed. Chapter 8: Inferences Based on a Single Sample: Tests of Hypotheses 9 Note: Null hypotheses are either rejected, or else there is insufficient evidence to reject them. (I.e., we don’t accept null hypotheses.) 8.1: The Elements of a Test of Hypotheses • Null hypothesis ( H ): A theory about the values of one or more parameters • Ex.: H : μ = μ 0 (a specified value for μ) • Alternative hypothesis ( H a ): Contradicts the null hypothesis • Ex.: H : µ ≠ µ • Test Statistic : The sample statistic to be used to test the hypothesis • Rejection region : The values for the test statistic which lead to rejection of the null hypothesis • Assumptions : Clear statements about any assumptions concerning the...
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Chapter_08 - Chapter 8: Inferences Based on a Single...

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