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

When using z-tests what is known our population mean μ and standard deviation σ are

known 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 estimating variability

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

however, sample variability systematically underestimates population variability estimating standard deviation the old

the denominator was too big, will under estimate population variance estimating standard deviation the old way

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

this is called biasBias 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 be bigger than SD, better estimate of population SD (σ) estimating variability the new way

the denominator is smaller, accurately estimate population variance estimating variability the new way

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

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

this is need to accurately infer population variancedegrees of freedom isn-1 in the denominator is called degrees of freedomDegrees of freedom refers to the number of scores that are free to vary given

a known parameter Degrees of freedom refers to the number of scores that are free to vary given

a known parameter

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

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