mm7 - Howdoweuseconfidenceintervals&...

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      significance tests to make inferences from a  random sample about a population mean? significance tests to compare the means of  two populations?
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      Standard error: when the standard  deviation of a statistic is estimated from the  data (i.e. from a sample), the result is called  the  standard error of the statistic .  Standard error: the estimated average  deviation from the expected value of the  sample mean if the sample were repeated  over & over.
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     Standard error is based on the  t- distribution , not the standard normal (z)  distribution.
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      Because it’s based on sample data, the  t-distribution is less certain, less precise,  & thus more variable than the z- distribution.
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      Hence the t-distribution is flatter, or wider,  than the z-distribution, when N<=1000. approximates the z-distribution once sample  size reaches N=120.  When N>1000, then the t- and z- distributions are identical.
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     Put differently, the smaller the sample size  (i.e. the fewer the degrees of freedom*), the  wider (i.e. the less precise) the t-distribution is  relative to the z-distribution. * Recall that ‘degrees of freedom’ are the  amount of information available to estimate a  statistic.  The more df’s, the better.
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     This, then, is another reason to  have larger samples: so that the  t-distribution becomes more  tests can be more accurate.
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     The z-distribution is used when we know the  population’s standard deviation—which,  however, we virtually never know.  Almost always, then, we use the t- distribution, because  we are estimating a  statistic from sample data .
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    Confirm that there’s a different t- distribution for each  n – 1  distribution:   Check the t-distribution critical values in  Moore/McCabe/Craig (Table D, page T- 11) for each df.
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    increasingly approximates the z-distribution. identical.  See Table D (page T-11).
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    Standard error of the mean : when the  standard deviation of the mean is  estimated from  sample data (& thus the t- distribution is used).  Formula for the standard error of the 
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mm7 - Howdoweuseconfidenceintervals&amp;...

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