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Chapter Eight

# Chapter Eight - Lecture Notes Chapter Eight Inferences...

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Lecture Notes Chapter Eight: Inferences Based on a Single Sample: Test of Hypothesis Randall Miller 1 | P a g e 1. The Elements of a Test of Hypothesis Conclusions and Consequences for a Test of Hypothesis True State of Nature Conclusion 0 H True a H True Accept 0 H (Assume 0 H True) Correct decision Type II error (probability β ) Reject 0 H (Assume a H True) Type I error (probability α ) Correct decision Elements of a Test of Hypothesis 1. Null hypothesis ( 0 H ): A theory about the values of one or more population parameters. The theory generally represents the status quo, which we adopt until it is proven false. By convention, the theory is stated as 0 H : parameter = value. 2. Alternative hypothesis ( a H ): A theory that contradicts the null hypothesis. The theory generally represents that which we will accept only when sufficient evidence exists to establish its truth. 3. Test statistic : A sample statistic used to decide whether to reject the null hypothesis. 4. Rejection region : The numerical values of the test statistic for which the null hypothesis will be rejected. The rejection region is chosen so that the probability is α that it will contain the test statistic when the null hypothesis is true, thereby leading to a Type I error. The value of α is usually chosen to be small (e.g., .01, .05, or .10) and is referred to as the level of significance of the test. 5. Assumptions : Clear statements of any assumptions made about the population(s) being sampled. 6. Experiment and calculation of test statistic : Performance of the sampling experiment and determination of the numerical value of the test statistic. 7. Conclusion : a. If the numerical value of the test statistic falls into the rejection region, we reject the null hypothesis and conclude that the alternative hypothesis is true. We know that the hypothesis-testing process will lead to this conclusion incorrectly (a Type I error) only 100 % α of the time when 0 H is true.

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Chapter Eight - Lecture Notes Chapter Eight Inferences...

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