Question

A random sample of n = 700 observations from a binomial population produced x = 475 successes.

Give the best point estimate for the binomial proportion p. (Round your answer to three decimal places.)

p̂ =

Calculate the 95% margin of error. (Round your answer to three decimal places.)

±

Answer 1

Solution :

Given that,

n = 700

x = 475

= x / n = 475 / 700 = 0.679

Point estimate = 0.679

1 - = 1 - 0.679 = 0.321

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.679 * 0.321) / 700)

= 0.035

Margin of error is 0.035