Situation
Confidence Interval
1 mean
(  known)
x  z*
Significance Test
Conditions


SRS
Ho: µ = µo
n
Z
x  o

n
and



Population is stated normal, or
Large sample size (n ≥ 30), or
Approx. Linear Norm Prob Plot
and

1 mean
(  unknown)
xt
*
or

s
n
t
2 dependent means
(matched pairs)

Ho: µ = 0
df = n-1

Population
 10n

SRS
and
x  o
s
n




population is normal, or
large sample size (n ≥ 30), or
moderate sample size
(15≤ n≤ 30) with moderate skewness and no
outliers, or
small sample size (n< 15) with little skewness
and no outliers.

Two independent SRSs
and
2 independent
means
(  known)
x  x  z
1
*
2

2
1
n1


2
2
Ho: µ1 = µ2


n2
z

x1  x 2
12
n1

 22
n2




population is normal, or
large sample size
(n1,n2 ≥ 30), or
moderate sample size
(15≤ both n1 & n2 ≤ 30) with moderate
skewness and no outliers, or
small sample size (n1 and n2< 15) with
little skewness and no outliers


2 independent
means
(  unknown)
(x1 – x 2 )  t *
2
1
2
2
s
s

n1 n2
(use df smaller of n1–1 and
n2–1)
Ho: µ1 = µ2
x –x
t  12 2 2
s1 s2

n1 n2
Two independent SRSs
and




population is normal, or
large sample size
(n1,n2 ≥ 30), or
moderate sample size
(15≤ both n1 & n2 ≤ 30) with moderate
skewness and no outliers, or
small sample size (n1 and n2< 15) with
little skewness and no outliers
1 proportion
pˆ  z *
1. Population  10n
2. SRS
3. TOS: npo 10
Ho : p  po
pˆ (1 – pˆ )
n

z

p po

po 1 po 
n
CI:


n1 po   10

n p  10
  
n1 p 10




1. Two independent SRS’s
Ho : p1  p
2
pˆ1  pˆ 2  
z*
2 proportions
 2. Population  10n1, Population  10n2
n1 pˆ  5,n1 (1 pˆ )  5
n2 pˆ  5,n2 (1 pˆ )  5
p1  p2


 
 
 
 
p1 p p1 p where p  x1  x 2

 

n1  n 2


n1
n2
n1 pˆ1  5,n1 (1 pˆ1 )  5
CI:
n2 pˆ 2  5,n2 (1 pˆ 2 )  5


pˆ1 (1 pˆ1 ) pˆ 2 (1 pˆ 2 ) z 

n1
n 2 


Chi-Square
Ho:
3. TOS:

There is no association
between the row vars.

and column vars. in the
table.
Independence:
Two-Way Table
 
2
O  E 
1. SRS
2. All expected counts ≥ 1
3. No more than 20% of exp. counts are less
than 5.
2
E
df = (r–1)(c–1)
r = rows, c = columns

E
Chi-Square
Ho:

Goodness of Fit:
One-Way Table
rowtot  coltot
tabletot
There is no difference
between the
distributions.
(….is the same as…)
2  
O  E 
1. SRS
2. All expected counts ≥ 1
3. No more than 20% of exp. counts are less
than 5.
2
E
df = n-1

Regression slope
(µy =

Confidence Interval for the
slope  :
+ ßx)
b  t *SE b` with n-2 df


1
SE b 
1. Mean response
b
t
SE b
relationship with x
2. For each value of x:
 response y varies normally
 repeated
responses y are indep.1

 stdev (unknown) about the true reg. line is
constant for all x
s
x  x 
2

Repeated
 observations on the same individual are not allowed.

y
Ho: ß = 0
has a straight line