Question

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin error to four decimals

95% confidence; n=380, x=50

Answer 1

Solution :

Given that,

n = 380

x = 50

Point estimate = sample proportion = = x / n = 50/380=0.132

1 -   = 1- 0.132 =0.868

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   ( Using z table )

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

= 1.96 (((0.132*0.868) /380 )

E = 0.0340

Margin of error = E = 0.0340