Question

Out of 600 people sampled, 300 preferred Candidate A. Based on this, estimate what proportion of the voting population ( p ) prefers Candidate A. Use a 99% confidence level, and give your answers as decimals, to three places.

Answer 1

Solution :

Given that,

n = 600

x = 300

= x / n = 300 / 600 = 0.5

1 - = 1 - 0.5 = 0.5

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 * (((0.5 * 0.5) / 600) = 0.052582

=0.053 (rounded)

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.5 - 0.053 < p < 0.5 + 0.053

0.447 < p < 0.553

proportion of the voting population ( p ) prefers Candidate A is

(0.447,0.553)