Question

In a random sample of 440 U.S. adults, 76% said that they believe that the U.S. Congress fails to pass laws that benefit the lives of all Americans. Use these sample statistics to construct a 90% confidence interval for the proportion of all U.S. adults who believe that the U.S. Congress fails to pass laws that benefit the lives of all Americans.

Give your answers as decimals, rounded to three decimal places.

< p <

Answer 1

Solution :

Given that,

n = 440

= 0.76

1 - = 1 - 0.76 = 0.24

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.760 * 0.240) / 440 )

= 0.033

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.760 - 0.033 < 0.760 + 0.033

0.727 < p < 0.793

The 90% confidence interval for the population proportion p is : ( 0.727, 0.793 )