Assumptions / Conditions / Req. for Inference Procedures
Means, with  known: z-tests and z-intervals
1-sample z-test or
1) Data gathered properly: SRS (and/or from a randomized experiment)
2) Sampling distribution of x̄ is approx. normal:
-- population itself is given to be normal, OR
-- n > 30, CLT says x̄ is approx normally distributed, OR
-- check actual data for normality: NPP, histogram, boxplot.
confidence interval
z
2-sample z-test or
confidence interval
  
x  z* 
 n 
x 

n


1) Data gathered properly: indep SRS (and/or from a randomized experiment)
2) Sampling distribution of x̄ ‘s is approx. normal: (same as above)
z
x1  x 2
 12
n1

x1  x 2   z
 22
*
12
n1

 22
n2
n2

Means, with  UNknown: t-tests
and t-intervals

1-sample t -test or
confidence interval
OR matched-pairs t-test
1) Data gathered properly: SRS (and/or from a randomized experiment)
2) Sampling distribution of x̄ is approx. normal:
-- population itself is given to be normal, OR
-- n > 40, CLT says x̄ is approx normally distributed, OR
-- n > 15, with no outliers or strong skewness, OR
-- check data for normality: NPP, histogram, boxplot.
-- matched pairs: all of above for the list of DIFFERENCES.
3) df = n-1
t
2-sample t-test or
confidence interval

 s 
x  t * 
 n 
x 
s
n
1) Data gathered properly: indep SRS (and/or from a randomized experiment)
2) Sampling distribution ofx̄ ‘s are approx. normal (same as above)
3) df = SMALLER n -1, OR ugly number form calculator
z
x1  x 2
2
x1  x 2   t
2
s1
s
 2
n n2


*
s12 s2 2

n1 n2
Proportions: z-tests and z-intervals
1-sample z-test or
confidence interval
1) Data gathered properly: SRS (and/or from a randomized experiment)
2) Sampling distrib of p^ is approx normal:
-- population is at least 10 times larger than sample.
-- np and n(1-p) > 10
z
2-sample z-test:

2-sample z-interval:
pˆ  po
po (1 po )
n
pˆ  z*
p(1 p)
n
1) Data gathered properly: indep SRS (and/or from a randomized experiment)

2) Sampling distrib of p^ ‘s is approx normal:
-- population is at least 10 times larger than sample.
-- for both samples, np and n(1-p) > 5
3) plain ‘p’ is the POOLED proportion of successes
pˆ1  pˆ 2
z
 1 1 
p(1 p)  
n1 n 2 
1), 2), and 3) as above.

pˆ1  pˆ 2   z*
pˆ1 (1 pˆ1 ) pˆ 2 (1 pˆ 2 )

n1
n2
Chi-Square: Tests for Goodness-of-Fit and Independence

1) Data gathered properly: SRS (and/or from a randomized experiment)
2) all expected counts at least 1
3) no more than 20% of expected counts < 5
4) for test of indep: df = (r-1)(c-1). For GOF: df = n-1
5) for test of indep, Exp count = (row total)(column total) / (table total)
Obs - Exp 
2
2  
Exp
Linear Regression: t - test and CI for slope

1) Data gathered properly: SRS (and/or from a randomized experiment)
2) observations are independent
3) Relationship between variables is reasonably linear: PLOT IT!
4) df = number of data points – 2.
5) Use results from computer output!
b
b  t * SE b
t
SE b
FIRE UP! You WILL be successful!

