QuestionA researcher *** to estimate, with 99% *** *** population *** *** *** who *** condent
with their country's banking system. *** estimate must be *** within 2% *** *** *** *** No preliminary estimate is available. Find *** *** *** *** *** *** minimum *** *** *** using *** *** study that found *** 25% *** *** *** *** *** *** with *** *** banking system.
Solution
The *** *** *** *** *** size *** to *** *** *** is
n= *** *** *** pis the *** *** *** *** *** Z
= 2and
Eis *** *** *** error.
a. *** *** estimate *** *** Thus *** assume that p= *** *** .
Given *** margin *** error *** 0 :02 *** *** *** coecient *** 1 *** 0 :99 . *** *** 0 :01 .
The *** value *** ZisZ
= *** 2
:5758 .
The minimum sample *** *** to estimate the proportion is
n= *** p)
z E
2
= 0 *** 0:5) *** 0
:02 *** 4146 :716
4147 :
Thus, the *** of *** *** *** that the99% *** *** for *** proportion will *** *** of *** 0:02 .
b.
A prior *** found *** *** of the *** *** *** are *** *** their country's banking
system. *** p= 0 *** .
Given *** margin of error *** *** :02 *** The *** *** is 1 = *** *** *** *** is = *** *** *** critical value of ZisZ
= *** *** *** *** sample *** required to *** the *** is
n= p(1 *** E
2
= 0 *** 0:25)
2:5758 0
:02
2
= *** :037
3111 *** the sample *** *** 3111will *** that *** condence interval for the proportion *** *** *** of *** *** ***