Question

When 328 college students are randomly selected and surveyed, it is found that 122 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

	A) 0.328 < p < 0.416
	B) 0.320 < p < 0.424
	C) 0.310 < p < 0.434
	D) 0.303 < p < 0.441

Answer 1

Given that,

n = 328

x = 122

Point estimate = sample proportion = = x / n = 122/328=0.372

1 -   = 1- 0.372 =0.628

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.372*0.628) / 328)

E = 0.0687

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.372- 0.0687< p < 0.372+0.0687

0.303< p < 0.441

The 99% confidence interval for the population proportion p is : 0.303< p < 0.441