In: Statistics and Probability
A pollster wishes to estimate, with 99% confidence, the
proportion of people who believe the United States should pursue a
more aggresive foreign policy.
Find the minimum sample size necessary to achieve a margin of error
of less than 2%.
Solution :
a)
= 0.5
1 - = 0.5
margin of error = E = 0.02
Z/2 = 2.576
sample size = n = (Z / 2 / E)2 * * (1 - )
= (2.576 / 0.02)2 * (0.5 * 0.5)
= 4148
Minimum sample size is required = 4148
b)
= 0.35
1 - = 0.65
margin of error = E = 0.02
Z/2 = 2.576
sample size = n = (Z / 2 / E)2 * * (1 - )
= (2.576 / 0.02)2 * (0.35 * 0.65)
= 3775
Minimum sample size is required = 3775