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SP 225 Lecture 11 Introduction to Hypothesis Testing

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The Most Liberal Senator Article by the National Journal rated Senator Kerry as the most liberal member of the Senate during the 2004 Presidential Election Aid decision-making by simplifying large amounts of data Can be misapplied Can be an essential tool for interest groups

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Questions Explain the National Journal's methodology for determining its scores. What method do the authors use to reexamine the roll call data used by the National Journal? From a statistical point of view, what is the importance of the absentee data presented in Table 1 for the analysis of legislators voting records? What factors influence a legislators voting decisions? How do these issues complicate the interpretation of voting records? Explain the format and the purpose of the graphing technique employed in figures 1-4. According to Figure 3, where does President Bush stand in comparison with the members of the Senate for those 62 votes? What makes the authors uncertain of this rank order? Why do the authors maintain it is necessary to analyze President Bushs stated issue positions in order to interpret Senator Kerrys voting record properly? Using the results shown in figure 4, explain how selecting a larger set of voting decisions over a longer period of time results in a different rank ordering. What was your overall assessment of the validity of the National Journals liberal-to-conservative scorecard? Was the public well-served by the magazines publication of its analysis?

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Research Questions Are the elderly more likely to vote than the population as a whole? Do college graduates really make more money?

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Investigating Questions Compare group statistics to population statistics All data obtained through EPSEM sampling

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Evaluating Claims Reasons for differences between sample and population statistics: Sampling variability Genuine differences

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What CAN We Say? We can give the probability there are genuine differences

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Making Probability Statements We are 95% confident there is a difference in income between men and women Benadryl makes patients more drowsy than Claritin (95% confident)

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Example of Mean Test Nationally, the population as a whole watches 6.2 hours of TV per day. A random sample of 1,017 senior citizens reports watching an average of 5.9 hours per day with a standard deviation of.7. Is the there a difference between the amount of television senior citizens watch as compared to the population as a whole?

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Review of Scientific Method The Wheel of Science

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Hypothesis Testing 5 Step Process Making assumptions about meeting test requirements Stating the null and alternative hypothesis Selecting the sampling distribution and establishing the critical region Making a decision and interpreting the test results

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Test Requirements Randomly collected data Interval-ratio data Normally distributed or large sample size

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Null Hypothesis Always a statement of no difference The researchers belief is the alternative hypothesis Null hypothesis can be disproven but never proven

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Alternative Hypothesis Statement which is true when the null hypothesis is false

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Selecting a Distribution Currently, only use the normal distribution Size of the critical region determines the level of certainty desired Rejection region is the range of z-scores where the null hypothesis is rejected Alpha is the level of uncertainty

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Decision Making Criteria Probability of our observed statistic given the null hypothesis is true. Exact value is called a p-value

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SPSS Test Using SPSS and GSS test the following claims: Extreme liberals sampled in the GSS share the opinion of the general population when asked if homosexuals should be allowed to become teachers (colhomo). Extreme conservatives sampled in the GSS share the opinion of the general population when asked if homosexuals should be allowed to become teachers (colhomo).

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Essay In the GSS, respondents are asked to rank their ideological beliefs (polviews)on a scale from 1 to 7, where 1 represents extremely liberal and 7 represents extremely conservative. Choose one ideology, either extremely liberal or extremely conservative, and write an essay describing the difference in beliefs between people sampled in GSS rating themselves as extremely ideological and the general population. Use any three measures that show a significant difference. Complete a full hypothesis test for each variable including the hypotheses, result and conclusion. Staple all SPSS output and calculations to your final essay. (1-2 pages. Due in 1 week)

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Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.

Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests.

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