STAT 121 Exam Prep Questions Verified Answers
sampling distribution of x-bar
the distribution of all x-bar (sample means) values from all possible samples of the same size
from the same population.
p
population proportion
p-hat
sample proportion
mu
population mean
x-bar
sample mean
sigma
population standard deviation
s
sample standard deviation
what happens as the sample size of the sampling distribution increases?
as sample size increases, there is less variability, less spread, and a smaller SD
center of sampling distribution of x-bar
exact value - mean stays the same = population parameter = mu
spread of sampling distribution of x-bar
, exact value - standard deviation (sigma/sqrtn)
gets smaller as the sample size increases
shape of sampling distribution of x-bar
apply Central Limit Theorem
CLT
if you take a large (n>30) SRS of size n from any population, the shape of the sampling of x-bar
is approximately normal (CLT does not have to apply for the mean of a sampling distribution to
equal the mean of the population)
how to compute approximate probabilities associated with x-bar (sample mean)
use the standard normal table if CLT applies
shape of sampling distribution of x-bar for normal population
normal
shape of sampling distribution of x-bar for non-normal population
approximately normal by the CLT if n>30
if n<30 we do not have enough information to answer the question
why are sampling distributions important?
allow us to know uncertainty of sample results
tells us how "close" the sample statistic should be to the population parameter
what does a sampling distribution with lot of variability mean?
that if you took another sample, it's likely you would get a very different result
mean of sampling distribution of x-bar
exactly mu
standard deviation of sampling distribution of x-bar
sampling distribution of x-bar
the distribution of all x-bar (sample means) values from all possible samples of the same size
from the same population.
p
population proportion
p-hat
sample proportion
mu
population mean
x-bar
sample mean
sigma
population standard deviation
s
sample standard deviation
what happens as the sample size of the sampling distribution increases?
as sample size increases, there is less variability, less spread, and a smaller SD
center of sampling distribution of x-bar
exact value - mean stays the same = population parameter = mu
spread of sampling distribution of x-bar
, exact value - standard deviation (sigma/sqrtn)
gets smaller as the sample size increases
shape of sampling distribution of x-bar
apply Central Limit Theorem
CLT
if you take a large (n>30) SRS of size n from any population, the shape of the sampling of x-bar
is approximately normal (CLT does not have to apply for the mean of a sampling distribution to
equal the mean of the population)
how to compute approximate probabilities associated with x-bar (sample mean)
use the standard normal table if CLT applies
shape of sampling distribution of x-bar for normal population
normal
shape of sampling distribution of x-bar for non-normal population
approximately normal by the CLT if n>30
if n<30 we do not have enough information to answer the question
why are sampling distributions important?
allow us to know uncertainty of sample results
tells us how "close" the sample statistic should be to the population parameter
what does a sampling distribution with lot of variability mean?
that if you took another sample, it's likely you would get a very different result
mean of sampling distribution of x-bar
exactly mu
standard deviation of sampling distribution of x-bar
