PS296 Lecture Notes - Lecture 7: Sampling Distribution, Standard Deviation, Random Variable
Sampling Distributions
Sampling Distribution:
-a sampling distribution is the distribution of a statistic (ex mean) over repeated sampling
-it is a probability distribution showing how a statistic varies
-it is unbiased if its mean is equal to the population mean
-each sample must be randomly selected and come from a normally distributed population
-a statistic is biased when it systematically over or under estimates the parameter of interest
-always forms normal distribution when plotted and the bulk of the means will be very close to the
population mean
Sampling Error:
-the variability of a statistic from sample to sample due to chance
-the difference between the sample mean and population mean
-we expect statistics to vary somewhat from parameter of interest however sampling mean is not
systematic variance
Standard Error of the Mean:
-the standard deviation of the sampling distribution
-with a sampling distribution of the mean, instead of having a mean and standard deviation we have a
mean and standard error
-standard error = standard deviation (new terminology)
Document Summary
A sampling distribution is the distribution of a statistic (ex mean) over repeated sampling. It is a probability distribution showing how a statistic varies. It is unbiased if its mean is equal to the population mean. Each sample must be randomly selected and come from a normally distributed population. A statistic is biased when it systematically over or under estimates the parameter of interest. Always forms normal distribution when plotted and the bulk of the means will be very close to the population mean. The variability of a statistic from sample to sample due to chance. The difference between the sample mean and population mean. We expect statistics to vary somewhat from parameter of interest however sampling mean is not systematic variance. With a sampling distribution of the mean, instead of having a mean and standard deviation we have a mean and standard error. Find sampling distribution by drawing 2 random heights each time.
