Download Sample Standard Deviation Given a sample of n

Sample Standard Deviation
Given a sample of n measurements x1, x2, . . ., xn with
mean x , the sample standard deviation, s, is
(x1 " x ) 2 + (x 2 " x ) 2 + ...+ (x n " x ) 2
s=
n "1
!
!
Sample Proportions
If a sample of size n is selected from a population, then
the fraction of the sample that belongs to a particular
group is called the sample proportion and is given by
pˆ = (number in the sample that belong to the group)/n
Distribution of Sample Proportions
If samples of size n are taken from a population having a
population proportion p, then the set of all sample
proportions has mean and standard deviation given by
p(1" p)
mean = p and standard deviation =
.
n
Standard Error
If a representative sample of size n is taken from a
population, and if the sample proportion equals pˆ , then
!
the standard deviation of the set of all sample proportions
pˆ (1" pˆ
is approximately sˆ =
, which is known as the
n
!
standard error of the sample.
95% Confidence interval and Margin of Error
If a sufficiently large representative sample has sample
! pˆ and standard error sˆ , then the 95%
proportion
confidence interval for the population proportion is the
interval of numbers from pˆ " 2 sˆ to pˆ + 2 sˆ . The margin of
error for the confidence!interval is ±2 sˆ .
!
Population Z-Score
The population z-score of a measurement, x, is given by
!
!
x "µ
, where µ is the!population mean and σ is the
z=
#
population standard deviation.