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Unformatted text preview: 1 Week 8 Session Three Lecture notes (Chapter 20) Professor Esfandiari The objective of this lecture is to teach you about hypothesis testing through… • Statement of the null hypothesis in symbol and words. • Statement of the alternative hypothesis in symbols and words. • Testing of the null hypothesis for proportion in the population and demonstrating how this strategy relates to CLT and the normal model. • Calculation and interpretation of the P value and how it relates to hypothesis testing. • Showing how you can test the null hypothesis for the population proportion through construction of the confidence interval. Null hypothesis (H0) : The null hypothesis is a statement about a hypothesized population parameter. Examples are: Example one : The proportion of American public who cannot retire due to the poor economy and need to work till the age of 80 is 30%. We do not know for sure what this percentage is. We are assuming it is 30%. H0: P = 0.30 Example two: The average age at which the women with a graduate degree get married in the United States is 32 years. H0: μ = 32 Example three: Years of education is not a significant predictor of income. Or, the slope of the regression line for the prediction of income from years of education is equal to zero. H0: β 1 =0 (read as beta one and shows slope in the population) Example four : There is no relationship between years of teaching experience and effective teaching. Or, the correlation between years of teaching experience and effective teaching is equal to zero. H0: ρ = 0 (read as rho and shows correlation in the population) 2 Example five : There is no difference in the proportion of males and females who practice family law. H0: P (female) – P (male) = 0 Example six : There is no difference between the average salary of males and females who teach science at the high school level. H0: μ (female)- μ (male) = 0 In examples one and two we are dealing with a single parameter (P and μ ) and we are setting these parameters equal to a constant. In examples two and three we are setting a parameter that shows the relationship between two quantitative variables equal to zero. In examples five and six we are setting the difference between two parameters equal to zero. Reminder: The null hypothesis is about population parameter and not sample statistics. Sample statistics is known. It is wrong to write: H0: p^ = 0.30(Wrong) In order to decide whether the null is true or not, we need to test it. Once we test it, we could make two decisions: a) Reject it and conclude that it is not true b) Fail to reject it and conclude that it is false Alternative Hypothesis (Ha) : In order to test the null hypothesis we also need an alternative hypothesis which we show with Ha. Alternative hypothesis consists of the value of the parameter that we consider plausible if we reject the null hypotheses....
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- Fall '11