# STAT 1430 Lecture Notes - Lecture 23: Statistic, Sampling Distribution, Statistical Parameter

STAT1430.01–Lecture23–Binomial Distribution March 26, 2019

• Measuring Sampling Variability

o Find the distribution of all possible values of the sample statistic (from all possible

samples of size n)

o This is called the: Sampling Distribution

o Find its center (mean), spread (standard error) and shape

o Use this information to make inferences about the population parameter

• Sampling Distribution of a Statistic

o Take all possible samples size n from the population

o Find the statistic you need from each sample (i.e.

)

o Put all these sample statistics together.

• Sampling distribution of barX: mean

o

= and possible sample mean (from many samples of size n many possible

)

o

has its own average,

known :

o Mean of all sample means = mean of the population

• Sampling distribution of

: standard error

o Formula:

o What affects the standard error and how?

▪ As n increases decreases more precision in

means have less variability

▪ As increases also increases

▪ As diversity/variability in the population increases, variability in

increases also

• Sampling distribution of bars: shape

o Case 1:X has a Normal distribution with mean and standard deviation

o The shape of the distribution of X is: normal

o The shape of the sampling distribution of barX is: normal

▪ Smaller standard error

▪ Same mean

• Cereal box example