TESTS FOR MEANS
One-Sample Z
Test for
Means
  " mean "
Two-Sample Z
Test for
Means
1  " mean "
2  " mean "
One-Sample T
Test for
Means
  " mean "
Two-Sample T
Test for
Means
Matched
Pairs T Test
1  " mean "
2  " mean "
d  ”mean
difference” SPECIFY
ORDER
Key words: mean or average
random sample
 known
population is normal OR n  30
Ho :   #
two independent random samples
Ho : 1  2
Ha : 1  or  or  2
1 and  2 known
both populations are normal, both sample sizes
 30
random sample
 unknown
population is normal OR n  30 OR show a plot
and say plot shows no extreme skewness or
outliers
two independent random samples
1 and  2 unknown
both populations are normal OR both sample sizes
 30 OR show both plots and say plots show no
extreme skewness or outliers
two dependent random samples
 d unknown
population of differences is normal OR n  30 OR
do plot of differences and say plot of DIFFERENCES
shows no extreme skewness or outliers
Ha :   or  or  #
z
z
x 

n
( x1  x2 )  ( 1  2 )
 12
n1
Ho :   #
Ha :   or  or  #
t

 22
n2
x 
s
n
df = n - 1
Ho : 1  2
Ha : 1  or  or  2
t
( x1  x2 )  ( 1  2 )
s12 s2 2

n1 n2
df = from calculator
Ho : d  0
Ha : d  or  or  0
t
xd   d
sd
n
df = n – 1
TESTS FOR PROPORTIONS
One-Proportion Z-Test
p = “proportion”
random sample
independent observations
population  10*n
Ho : p  #
two independent random samples
both populations  10n
Ho : p1  p2
Ha : p  or  or  #
z
np and n(1  p)  10
Two-Proportion Z-Test
p1  " proportion "
p2  " proportion "
n1 pˆ and n1qˆ and n2 pˆ and n2 qˆ  5 or 10
pooled pˆ 
x1  x2
n1  n2
Key words: proportion, percentage, part out of whole
Ha : p1  OR  OR  p2
z
p̂  p
pq
n
pˆ1  pˆ 2
1 1
ˆ ˆ  
pq
 n1 n2 
CHI SQUARE TESTS
Chi Square Goodness of
Fit Test
look out for percentages, ratios or
uniform distribution;
use lists in calculator and sum(L3) to
get test statistic
random
sample;
counts are
independent;
all expected
counts  5
Ho: the
distribution
is the same
as the
hypothesized
distribution
(observed  exp ected ) 2
exp ected
df  n  1 where n is # of CATEGORIES
2  
Ha: the
distribution
is not the
same as the
hypothesized
distribution
Chi Square Test of
Independence
look out for ASSOCIATION or
RELATIONSHIP or DEPENDENT
with CATEGORICAL variables; one
sample
random
sample;
counts are
independent;
all expected
counts  5
Ho: there is
no
association
between the
variables
Ha: there is
an
association
between the
variables
(observed  exp ected ) 2
exp ected
df  (r  1)(c  1)
2  
Chi Square Test of
Homogeneity
look out for DIFFERENCE in
proportions with more than two
categories; two or more independent
samples
Independent
random
samples;
counts are
independent;
all expected
counts  5
Ho: the
proportions
are all the
same
2  
(observed  exp ected )2
exp ected
df = (r-1)(c-1)
Ha: the
proportions
are not all
the same
T TEST FOR SLOPE (REGRESSION)
T Test for Slope of a
Regression Line
look out for ASSOCIATION or RELATIONSHIP or
DEPENDENT with
two QUANTITATIVE variables
residuals are normally
distributed;
x and y have a linear
relationship
constant variance in y
Key words: association, correlation, relationship, predict – QUANTITATIVE VARIABLES
Ho : 1  0
Ha : 1  0
t
b1
SEb1
df = n - 2