Question

If n=560 and p' (p-prime) = 0.87, construct a 99% confidence interval.

Give your answers to three decimals.

Answer 1

Solution :

Given that,

n = 560

= 0.87

1 - = 1 - 0.87 = 0.13

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

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

= 2.576 * (((0.87 * 0.13) / 560)

= 0.037

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.87 - 0.037 < p < 0.87 + 0.037

0.833 < p < 0.907

(0.833,0.907)

The 99% confidence interval 0.833 to 0.907