6.4 sampling distributions and estimators Flashcards
what is a sampling distribution of a statistic?
the distribution of all values of the statistic when all possible samples of the same size “n” are taken from the same population
what is the sampling distribution of the sample mean?
the distribution of all possible sample means (or the distribution of the variable xbar) with all samples having the same sample size “n” taken from the same population
sample means _______ the value of the population mean
target
the distribution of the sample means tends to be
a normal distribution
what is the sampling distribution of the sample variance?
the distribution of all possible sample variances (or the distribution of the variable S^2) with all samples having the same sample size “n” taken from the same population
do the sample variances target the value of the population variance?
yes
the distribution of sample variances tends to be
skewed to the right
what is the sampling distribution of the sample proportion?
the distribution of all possible sample means (or the distribution of the variable p-hat) with all samples having the same sample size “n” taken from the same population
the mean of the sample proportion is equal to
the population proportion
does the distribution of sample proportions tend to approximate a standard distribution?
yes
what is an estimator?
an estimator is a statistic used to infer the value of a population parameter
what is an unbiased estimator?
an estimator that targets the value of the population parameter (the sampling distribution has a mean that is equal to the population value of the corresponding parameter)
what are the unbiased estimators?
xbar (mean)
sample variance (S^2)
proportion (p-hat)
what are the biased estimators?
median range standard deviation (s)
