Question

Out of 600 people sampled, 204 preferred Candidate A. Based on this, find a 99% confidence level for the true proportion of the voting population ( p ) prefers Candidate A. Give your answers as decimals, to three places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 204 / 600 = 0.340

1 - = 1 - 0.340 = 0.66

Z/2 = 2.576

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

= 2.576 * (((0.340 * 0.66) / 600)

Margin of error = E = 0.050

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.340 - 0.050 < p < 0.340 + 0.050

0.290 < p < 0.390

The 99% confidence interval for the population proportion p is : 0.290 , 0.390