Question

1. When 258 college students are randomly selected and surveyed, it is found that 106 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

a.0.351 < p < 0.471

b.0.332 < p < 0.490

c.0.339 < p < 0.482

d.0.360 < p < 0.461

Answer 1

Solution :

Given that,

n = 258

x = 106

= x / n = 106 / 258 = 0.411

1 - = 1 - 0.411= 0.589

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.411 * 0.589) / 258 )

= 0.079

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.411 - 0.079 < p < 0.411 + 0.079

0.332 < p < 0.490

Option b ) is correct.