Page 83 - DMGT404 RESEARCH_METHODOLOGY

Unit 4: Sampling Design

Standard error = X = 3.69 Notes
We know that


X =
n
 2
 X =
2 n

 2  12  2
 n = 2   
 X  3.69 
 n = 10.57 11

Example: Determine the sample size, if sample proportion p = 0.4 and standard error of
proportion is 0.043.
Solution:
Given that p = 0.4 1  q = 0.6  = 0.043
p
pq
We know that  =
p
n
pq
  2 p =
n
pq 0.4 0.6

 n = 
 2 p (0.043) 2
= 129.79 130

Example: Determine the sample size if the standard deviation of population is 8.66, sample
mean is 45, population mean 43 and the desired degree of precision is 95%.
Solution:

Given that  = 43, X  45
 = 8.66 z = 5% l.o.s

 z = 1.96

We know that sample size n can be obtained using the relation
2
 z  
n =   
 d 

where d =   X
2

 1.96 8.66 
n =    72.03 72

 43 45 


LOVELY PROFESSIONAL UNIVERSITY 77