Question

Find the margin of error for the 95% confidence interval used to estimate the population proportion.

In a sample of 178 observations, there were 100 positive outcomes.

Group of answer choices

0.0656

0.128

0.00271

0.0729

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 100 / 178 = 0.562

1 - = 1 - 0.562 = 0.438

Z_/2 =   Z0.025 = 1.96

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

= 1.96 * (((0.562 * 0.438) /178 )

E = 0.0729

A 95% Margin Of Error = 0.0729 ,   Option 4th is correct