Question

According to a poll, 78% of California adults (393 out of 506 surveyed) feel that education is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education is one of the top issues facing California.

What is a point estimate for the true population proportion?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.78

1 - = 1 - 0.78 = 0.22

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.78 * 0.22) / 506)

= 0.030

A 90% confidence interval for population proportion p is ,

± E  

= 0.78  ± 0.030

= ( 0.750, 0.810 )