Question

In a survey of 2332 adults, 711 say they believe in UFOs.

Construct a 95% confidence interval for the population proportion of adults who believe in UFO's.

A 95% confidence interval for the population proportion is

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 711 / 2332 = 0.305

1 - = 1 - 0.305 = 0.695

Z_/2 = Z0.025 = 1.96

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

  = 1.96 * (((0.305 * 0.695) / 2332)

= 0.019

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.305 - 0.019 < p < 0.305 + 0.019

0.286 < p < 0.324

The 95% confidence interval for the population proportion p is : ( 0.286 , 0.324 )