When using z-tests what is known<span>our population mean μ and standard deviation σ are known</span>We used z-test to ask ifour sample mean is different than the population mean.student's t-tests akaone-way t-testsOne-way t-tests compare asample mean to a population mean but allows you to estimate population variability when it is not providedS=estimated population standard deviationSm =estimated standard deviation of the sampling distribution, based on Sgreek letters=population parametersroman letters=based on our sample<span>estimating variability
We measure sample variability and use it to</span>estimate population variability<span>We measure sample variability and use it to estimate population variability
however, sample variability systematically</span>underestimates population variability<span>estimating standard deviation the old
the denominator was</span>too big, will under estimate population variance<span>estimating standard deviation the old way
SD is</span>too small estimate population SD (σ)<span>However, sample variability systematically underestimates population variability
this is called</span>biasBias occurs when asample statistic systematically differs from a population statisticBias can be due topoor design, non-random sampling, etc.<span>estimating variability the new way
S will be</span>bigger than SD, better estimate of population SD (σ)<span>estimating variability the new way
the denominator is</span>smaller, accurately estimate population variance<span>estimating variability the new way
S will be</span>bigger than SD, better estimate of population SD (σ)<span>estimating variability
SD^2 is calculated with what in the denominator</span>n in denominator is biased as an estimatorS^2 calculated with what in denominatorn-1 in denominator is unbiased<span>S^2 calculated with n-1 in denominator is unbiased
this is need to</span>accurately infer population variancedegrees of freedom isn-1 in the denominator is called degrees of freedomDegrees of freedom refers to the<span>number of scores that are free to vary given a known parameter</span><span>Degrees of freedom refers to the number of scores that are free to vary given a known parameter
here we assume</span>sample mean = population meanIn order to ensure that sample mean = population mean all butone score is free to vary<span>n-1 scores in our sample can vary
The one score that doesn't vary ensures that our</span>sample mean will equal our population mean<span>Estimating one parameter in one-</span>
