Question

In a random sample of 509 people, only 138 correctly described the Bill of Rights as the first 10 amendments to the U.S. Constitution. Calculate a 99% confidence interval for the proportion of the entire population that could give a correct description. (Use the value of z rounded to two decimal places. Round your answers to three decimal places.)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 138 / 509 = 0.271

1 - = 0.729

Z/2 = 2.58

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

= 2.58 * [(0.271 * 0.729) / 509]

= 0.051

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.271 - 0.051 < p < 0.271 + 0.051

0.220 < p < 0.322

(0.220, 0.322)