Question

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a random sample (assume it is an SRS) of registered voters. Let p represent the proportion of registered voters in the state that would vote for the Republican candidate. How large a sample n would you need to estimate p with margin of error 0.03 with 99% confidence

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.03

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.03)² * 0.5 * 0.5

= 1843.41

= 1843

n = sample size = 1843