Question

Out of 400 people sampled, 316 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A. Use a 95% confidence level, and give your answers as decimals, to three places

Answer 1

Solution :

n = 400

x = 316

= x / n = 316 / 400 = 0.790

1 - = 1 - 0.790 = 0.210

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.960* (((0.790 * 0.210) / 4900)

= 0.040

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.790 - 0.040 < p < 0.790 + 0.040

0.750 < p < 0.830