Question

It is believe that slightly over 65% of Americans own pets. How large a sample is necessary to estimate the true proportion within 0.02 with 90% confidence?

How large a sample is needed if you had no prior knowledge of the proportion?

Answer 1

Solution :

Given that,

= 0.65

1 - = 1 - 0.65 = 0.35

margin of error = E = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 / 0.02)² * 0.65* 0.35

=1539.05

Sample size = 1539