Question

If n=240 and ˆ p (p-hat) = 0.58, construct a 99% confidence interval. Give your answers to three decimals

Answer 1

Solution :

Given that,

n = 240

Point estimate = sample proportion = = 0.58

1 - = 1-0.58=0.42

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 (((0.58*0.42) / 240)

= 0.082

A 99% confidence interval is ,

- E < p < + E

0.58-0.082 < p < 0.58+0.082

0.498< p < 0.662

(0.498,.662)