mm8 - Lasttimewediscussedttests:howto...

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 Last time we discussed t-tests: how to  use  sample means of quantitative  variables  to make inferences about  parameters.  Today we’ll use the very same  principles, but we’ll do tests to use  sample proportions of categorical  variables  to make inferences about  parameters.
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 E.g., a random sample of households in a  poor neighborhood in Lima, Peru, finds that  38% of the households are headed by single  women.  Is this neighborhood proportion  representative of the population proportion  of Lima poor neighborhoods), or is it  different enough to test statistically  significant?
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 E.g., since a non-government organization  subsidies to women in a poor neighborhood  in Buenos Aires, a random sample finds that  the neighborhood’s proportion of income- earning adult women has increased from  34% to 39%.  Is this after vs. before proportion due to  sampling variability? Or is it different enough  to be statistically significant?
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 The same random sample finds that 41%  of the sampled women who participated in  who didn’t participate are now engaged in  income-earning activities.  Is this difference in proportions due to  sampling variability?  Or is it different  enough to be statistically significant?
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  Sample proportion: a binomial  count within a sample divided by  the sample size- n.   It is a  categorical  variable (e.g.,  yes vs. no; lived vs. died)   Sample Proportion
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    Premises   Random sample of independent observations.  Binomial (i.e. ‘success’/’failure’) count.  The population must be at least 10 times larger  than the sample.  There must be at least 10 observations for  p at least 10 observations for  1 – p.
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  If these sample assumptions are met,  then  the difference between the two  proportions being compared  (e.g.,  observed proportion vs. benchmark;  two-sample proportions; after vs.  before proportion)  is approximately  standard normal in distribution.
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 Moore/McCabe use a more precise than 
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mm8 - Lasttimewediscussedttests:howto...

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