Question

Find the margin of error and​ 95% confidence interval for the survey result described.

According to a poll of

747

​people, about​ one-third

​(33​%)

of Americans keep a dog for protection.

Margin of

error equals= __%

​(Round to the nearest whole number as​ needed.)Confidence interval is from

___%

to

___%.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.33

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

= 1.96 (((0.33 * 0.67) / 747)

= 0.034

= 3.4%

A 95% confidence interval for population proportion p is ,

± E

0.33 ± 0.034

0.296 , 0.364

29.6%, 36.4%