Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal places.

When

267267

college students are randomly selected and​ surveyed, it is found that

101101

own a car. Find a​ 99% confidence interval for the true proportion of all college students who own a car.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 101 / 267 = 0.378

1 - = 1 - 0.378 = 0.622

Z/2 = 2.576

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

= 2.576 * (((0.378 * 0.622) / 267)

Margin of error = E = 0.076

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.378 - 0.076 < p < 0.378 + 0.076

0.302 < p < 0.454

The 99% confidence interval for the population proportion p is : 0.302 , 0.454