Question

an urban economist wishes to estimate the proportion of americans who own their homes. what size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if (a) he uses a 2010 estimate of 0.669 obtained from the u.s. census bureau

Answer 1

The sample size for the given problem is 1499.

What is sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Given:

An urban economist wishes to estimate the proportion of Americans who own their homes.

p cap = 0.669

1 - p cap = 0.331

margin of error = E = 0.02

 $Z_a_l_p_h_a_/_2$= 1.645

Sample size = n

$n = (Z_a_l_p_h_a_/_2/E)^2*Pcap*(1 - Pcap)\\= (\frac{1.645}{0.02})^2*0.669*0.331\\ = 1499$

Hence, the sample size for the given problem is 1499.

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