Question

You wish to estimate, with 95% confidence the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. Your estimate must be accurate within 5% of the population proportion. a) Find the minimum sample size required when no preliminary estimate is available. b) Find the minimum sample size required using a prior survey that found that 31% of motor vehicle fatalities were caused by alcohol impaired driving.

Answer 1

Sample size = Z²/2 * p(1-p) / E²

a)

When prior estimate for proportion is not available then p = 0.50

Sample size = 1.96² * 0.50 * 0.50 / 0.05²

= 384.16

n = 385 (Rounded up to nearest integer)

b)

Given , p = 0.31

Sample size = 1.96² * 0.31 * 0.69 / 0.05²

= 328.69

n = 329 (Rounded up to nearest integer)