Question

The figure at the right is from a survey of 498 U.S. adults. Construct a 90% confidence interval for the population proportion of U.S. adults who think that teenagers are the more dangerous drivers. The figure basically shows that:

Teenagers = 71%

People over 65 = 25%

No opinion = 4%

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.71

1 - = 1 - 0.71 = 0.29

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.71 * 0.29) / 498 )

= 0.033

A 90% confidence interval for population proportion p is ,

± E

= 0.71  ± 0.033

= ( 0.677, 0.743 )