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Exam 3 Notes.docx

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Michigan State University
SOC 282

Exam 3 Notes 2.25.14 Chapter 9: Testing Hypotheses • Overview o Intro videos o Five fundamental steps in hypothesis testing o Null hypothesis o Alternative hypothesis o One and two-tailed tests o Type I and II errors o Testing the difference between two means o T tests 3.10.14 • One and two-tailed tests o 95% confidence interval  One tailed = Z-score of 1.645 • Example: women’s earnings are lower than men’s earnings  Two-tailed = z-score of 1.96 • Example: there is a difference between the statistics grades of business majors and economics majors o Z-score = sample mean minus population mean divided by standard error  If population standard deviation is not known we can use t • T represents the number of standard errors that our sample is from the population mean assuming that out null hypothesis is true. o T statistics uses degrees of freedom in order to calculate the level of significance (page 497 is Appendix C and 269 has shorter version of table) o As the number of degrees of freedom (df) increases, t gets closer to Z o For an alpha level of 0/05 (two tailed) t = Degrees of freedom Level of significance (2 tailed)= .05 1 12.706 4 2.776 10 2.228 60 2.000 120 1.980 Z (or t with df = infinity) 1.960 o You cannot use a z score if you don’t know the population standard deviation o You can use a t score when you don’t know the population standard deviation 3.11.14 • Creating the hypothesis test (pg. 264) o Make assumptions  Sample is random  The variable is interval-ratio level of measurement  If N is sufficiently large, you can use Z instead of t (this usually means N>30, the book mentions N>50) o State the research and null hypothesis and select alpha  Research hypothesis symbolized as H1 (Ha) and null as H0  Express the hypotheses in terms of population parameters o Select the sampling distribution and specify the test statistics  If N is low, use t and degrees of freedom.  If N is high, use a Z-score o Compute the test statistic o Make a decision and interpret results  IS P IS LOW (or you have a high Z-score): REJECT THE NULL HYPOTHESIS! • Null and alternative hypotheses o In hypothesis testing we set up two hypotheses (null and research) o The null hypothesis (H0) is a statement of no difference (or equality)  The GPA of business majors is equal to that of econ majors  Women’s salaries are equal to or greater than men’s o The research (alternative) hypothesis (Ha) is the complement to the null o It is the hypothesis you are interested in  The GPA of business majors is not equal to that of econ majors  Women’s salaries are less than men’s o We do not prove our research hypothesis o We reject the null hypothesis (thus giving support to our research hypothesis) o Two types of errors we might commit:  Type I: rejecting a hypothesis that is true  Type II: failing to reject a hypothesis that is false o The probability of committing a type I error is the alpha level  When we set alpha to .05, we mean that there is a 5% chance of rejecting a null hypothesis that is actually true. o We set the alpha level based on the risk (of rejecting a true null hypothesis) that we are willing to accept  .01 and .001 represent higher levels of confidence 3.12.14 • One tailed tests have directional research hypotheses • Two tailed tests have non-directional research hypotheses 3.17.14 • Non directional hypotheses use a two tailed test • For directional hypotheses use a one tailed test 3.18.14 Chapter 10: Cross Tabulating Data • Exam 3 over chapters 9, 10, and 11 • Outline o Independent and dependent variables o Constructing a bivariate table o Computing percentages in a bivariate table o Dealing with ambiguous relationships between variables o Reading the research literature o Propertied of a bivariate relationship o Elaboration o Statistics in practice • The variable you want to explain is the dependent variable and the variable doing the explaining is the independent variable o Is there a relationship o What is the direction of the relationship o What is the strength of the relationship • Bivariate analysis: a statistical method designed to detect and describe the relationship between two variables • Cross-tabulation: a technique for analyzing the relationship between two variable that have been organized in a table o Example: if we hypothesize that English proficiency varies by whether person is native born or foreign born, what is the independent variable and the dependent variable?  Independent: nativity  Dependent: English proficiency o Independent variable is in the columns while the dependent variable is in the rows and read the table in the opposite direction meaning independent variable is read across the rows and the dependent variable is read along the columns 3.19.14 • Determining the strength of the relationship o A quick method is to examine the percentage difference across the differe
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