Studied by 13 peopleparameter
a number that describes some characteristic of the population
statistic
a number that describes some characteristic of the sample
sampling variability
the value of a statistic varies in repeated random sampling; we need to estimate sampling variability so we know how close our estimates are to the truth (margin of error).
sampling distribution
the distribution of values taken by the statistic in all possible samples of the same size from the same population
distribution
describes possible values and how often they occur
distribution of the population
gives the values of the variable for all individuals in the population
ex. proportion of all pennies minted in 2000s
distribution of sample
shows the values of the variable for the individuals in the sample
ex. proportion of pennies in your individual sample minted in 2000s
sampling distribution of a sample statistic
describes how a statistic varies in many samples from the population
ex. the proportion of pennies minted in 2000s from all samples
unbiased estimator
mean of the sampling distribution of a statistic is equal to the true value of the parameter
what are biased estimators?
range, standard deviation
what are unbiased estimators?
mean, IQR, variance
biased estimator
statistic is consistently higher or lower than the parameter
how can you reduce the variability of a statistic?
bigger sample size
better design (stratified sampling)
what effect does the size of the population have on the variability of a statistic?
not much, as long as the population is at least 10x the sample (10% condition)
what is the difference between accuracy and precision?
accurate = unbiased
precise = low variability
when is it OK to say that the distribution of phat is approximately Normal?
np and n(1-p) are at least 10
sampling distribution of a sample proportion
shape: as n increases, the sampling distribution of sample proportions becomes approximately Normal.
center: µphat = p
spread: σphat = √p(1-p)/n if the 10% rule applies
sampling distribution of a sample mean
µxbar = µ
σxbar = σ/√n, n ≤ 1/10N
what is the shape of the sampling distribution of a sample mean when the sample is taken from a Normally distributed population?
always normal, regardless of size
central limit theorem
for large samples, xbar sampling distribution will be approximately normal; for small samples, it will resemble the shape of the original population.
n ≥ 30
Note
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