Lecture11

# Lecture11 - Lecture 11 Compared to what Hypothesis test for...

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1 Lecture 11 Compared to what? Hypothesis test  for a proportion

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2 Overview • You’ve learned hypothesis tests for a mean • Today you’ll learn hypothesis tests for a proportion • Connection A proportion is the mean of a dummy variable
3 1. What are the hypotheses?

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4 Research question • Who will win Ohio? • Bush or Kerry?
5 Parameter • Hypothesis = Claim about a  parameter Today: claim about the population proportion π . E.g., proportion of voters that favors Bush Population: Voters choosing Bush or Kerry need a majority to win the state • Two alternatives:  winning.) is Kerry or Bush (Either .5. not is Bush voting proportion that the ) : ( is ) ( hypothesis research The 5 . : tied.) is (Ohio .5. is Bush voting proportion that the ) : ( is ) ( hypothesis null The 5 . : 1 1 0 0 π π π π H H H H = One tail or two?

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6 2. Hypothesis tests
7 Hypothesis test: Definition • Given evidence from a  sample , we test (decide whether to reject) the null hypothesis about the population

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8 Sample • RasmussenReports.com • Sample of 500 Likely Ohio Voters, March 14-16, 2004 Bush 41%, Kerry 45%, Other 4%, Not Sure 10% Ignore “other”, “not sure” Remaining: N =430, p =.477 favor Bush, 1- p =.523 Kerry • Most of the  sample  favors Kerry But the hypothesis asks about the population which is probably different (sampling error)
9 2a. Hypothesis test: Sampling distribution method

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10 Hypothesis test: Sampling distribution method If H 0  were true what would the sampling distribution look like (null distribution)?
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