Sampling Distribution of the Sample Means
Suppose that a variable x of a population has a mean  and standard deviation  .
Then, for samples of size n,
  = 

●  =
n
 The distribution  is normally distributed when the populations are normally
distributed or the samples are large. (n ≥ 30)
The Sampling Distribution of the Sample Proportion
For samples of size n,

 p (1 p )
● 
p = p
n
p
 The distribution of p is approximately normally distributed for large n.
(When we say that n is large, we mean that np and n(1-p) are both 5 or greater)
The Sampling Distribution of the Difference Between Two Sample Means for
Independent Samples
Suppose that x is a normally distributed variable on each of two populations. Then,
for independent samples of sizes n1 and n2 from the two populations,

x1 x2  1  2
●
 x1 x2  ( 1 )2  ( 2 )2
n1
n2
 The distribution x1  x2 is normally distributed when the populations are
normally distributed or the samples are large. ( ni ≥30)
The sampling Distribution of the Difference Between Two Sample Proportions
for Large and Independent Samples
For independent samples of sizes n1 and n2 from the two populations,

 p  p  p1  p2
1

2
●  p p 
1
2
p1 (1  p1 ) p2 (1  p2 )

n1
n2
p1  p2 is approximately normally distributed for large n1 and n2
(When we say that n is large, we mean that np and n(1-p) are both 5 or greater)
Refer to the chart with formulas
Write all the formulas on the space provided below
 Look at the formulas for constructing confidence intervals and notice the
pattern
Point estimate ± Critical Value * standard deviation of the distribution
 Look at the formulas for finding the test statistic (z or t score) and notice the
pattern
Z (or t) score = (score – mean) / standard deviation of the distribution