Question

Out of 200 people sampled, 156 preferred Candidate A. Based on this, estimate what proportion of the voting population ( p p ) prefers Candidate A. Use a 99% confidence level, and give your answers as decimals, to three places.

Answer 1

Solution :  

Given that,

n = 200

x = 150

Point estimate = sample proportion = = x / n = 150 / 200 = 0.75

1 - = 1 - 0.75 = 0.25

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.9 = 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 * (((0.75 * 0.25) / 200)

= 0.079

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.75 - 0.079 < p < 0.75 + 0.079

0.671 < p < 0.829

The 99% confidence interval for the population proportion p is : 0.671 , 0.829