Question

Colorado voted recently on legalizing recreational marijuana use. Prior to the election,

pollsters working in favor of legalization wanted to estimate the proportion of California

voters that were in favor of the proposed law. The pollsters wanted a margin of error of 0.01 and a confidence level of 95% for their estimate.

1. What sample size did they need? (Assume p* or  = 0.5.)
2. The pollsters’ budget was not big enough to accommodate a sample of that size. So, instead, they decided to go for a margin of error of 0.05. What sample size do they need? (Again, assume p* or  = 0.5.)

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.01

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.01)² * 0.5 * 0.5

= 9064

Sample size = 9064

The pollsters’ budget was not big enough to accommodate a sample of that size. So, instead, they decided to go for a margin of error of 0.05

margin of error = E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.05)² * 0.5 * 0.5

= 384.16

Sample size = 384