Question

On average, a sample of n = 16 scores from a population with s = 10 will provide a better estimate of the population mean than you would get with a sample of n = 16 scores from a population with s = 5.
a. True
b. False

Answer 1

When using z-tests what is knownour population mean μ and standard deviation σ are
knownWe 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 sampleestimating variability

We measure sample variability and use it toestimate population variabilityWe measure sample variability and use it to estimate population variability

however, sample variability systematicallyunderestimates population variabilityestimating standard deviation the old 

the denominator wastoo big, will under estimate population varianceestimating standard deviation the old way

SD istoo small estimate population SD (σ)However, sample variability systematically underestimates population variability

this is calledbiasBias occurs when asample statistic systematically differs from a population statisticBias can be due topoor design, non-random sampling, etc.estimating variability the new way 

S will bebigger than SD, better estimate of population SD (σ)estimating variability the new way 

the denominator issmaller, accurately estimate population varianceestimating variability the new way 

S will bebigger than SD, better estimate of population SD (σ)estimating variability

SD^2 is calculated with what in the denominatorn in denominator is biased as an estimatorS^2 calculated with what in denominatorn-1 in denominator is unbiasedS^2 calculated with n-1 in denominator is unbiased

this is need toaccurately infer population variancedegrees of freedom isn-1 in the denominator is called degrees of freedomDegrees of freedom refers to thenumber of scores that are free to vary given
a known parameterDegrees of freedom refers to the number of scores that are free to vary given
a known parameter

here we assumesample mean = population meanIn order to ensure that sample mean = population mean all butone score is free to varyn-1 scores in our sample can vary

The one score that doesn't vary ensures that oursample mean will equal our population meanEstimating one parameter in one-