Question

Suppose you wish to estimate a population proportion p based on sample of n observations. What sample size is required if you want your estimate to be within .03 of p with probability equal to 0.90?

a. 752 b. 423 c. 1,068 d. 1.529 e. none of these

Answer 1

Solution :

Given that,

= 0.90

1 - = 1 - 0.90= 0.1

margin of error = E = % = 0.03

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

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

= (1.645 / 0.03)2 * 0.90 * 0.10

=271

Sample size = 271