Download Random Variable of interest

Univariate Inference Formulas Tabulated
Type of Variable
Parameter of Interest
Estimator (Sample Statistic)
Standard Error of the Estimator, SE
Qualitative Categorical
Quantitative Measurement, Xi
Population proportion, 
Population mean, Xi
sample proportion,
 frequency of category 
p
 sample size, n 
sample mean,
 sample sum 
X
 sample size, n 
SE  p  
Assumptions about the underlying
distribution
p 1  p  n
SE  X   
n
(i) Population SD, ,
known
None
(ii) Xi ~ Normal, or n large
Confidence Interval Estimation
Critical Value, CV,
for confidence level = (1 )
Margin of Error
(MOE) = (CV)(SE)
100(1 )% Confidence Limits
= (Estimator)  (MOE)
Reference
Golde Holtzman
all rights reserved
n
(i) Xi ~ Normal (really
need only symmetry)
To estimate 
To estimate σ known
To estimate σ unknown
Standard Normal, z* = z1 2
Standard Normal, z* = z1 / 2
Student’s T, t* = tn1,1 / 2
 z *
 z * 
p 1 p  n
p   z * p 1  p  n
H0: φ  φ0
Significance/Hypothesis Testing
Test Criterion/Test Statistic
 Estimator    Hypothetical Value 

SE
estimated SE  X   s
Z
n
X   z *

 t *  s
n
X   t * s
H0: µ µ0
p  0
0 1  0  n
P-value on T-Table, df = ∞
B&M Chapter 19
Z
X  0
 n
P-value on T -Table, df = ∞
B&M Chapters 14 and 15
Page 1
n

n
H0: µ  µ0
Tn 1 
X  0
s n
P on T -Table, df = (n – 1)
B&M Chapter 17
5/8/2013
UnivariateFormulasTable.pdf
Univariate Inference Formulas Tabulated
Type of Variable
Parameter of Interest
Estimator (Sample Statistic)
Standard Error of the Estimator, SE
Quantitative Measurement, Xi
Population Standard Deviation, =
Xi
sample standard deviation, s, calculated from the sample electronically
SE(s) has no role in estimation or hypothesis testing of 
Assumptions about the underlying
distribution
Xi ~ Normal (really need only symmetry)
Confidence Interval Estimation
To estimate σ
Critical Values, CV
Margin of Error
Confidence Limits
Pearson’s Chi-Squared,  n21,1 2 and  n21, 2
MOE has no role in confidence interval for 




 n  1 s 2 ,
 n21,1 2
 n21, 2 

H0: σ σ0
Significance/Hypothesis Testing

Test Criterion/Test Statistic
Golde Holtzman
all rights reserved
 n  1 s 2 
Page 2
2
n 1
  n  1
s2
 02
5/8/2013
UnivariateFormulasTable.pdf