Question

Construct a confidence interval of the population proportion at the given level of confidence.

x equals 45 comma n equals 150 comma 95 % confidencex=45, n=150, 95% confidence

Answer 1

Solution :

Given that,

n = 150

x = 45

Point estimate = sample proportion = = x / n = 45 / 150 = 0.300

1 - = 1 - 0.300 = 0.700

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.300 * 0.700) / 150)

= 0.073

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.300 - 0.073 < p < 0.300 + 0.073

0.227 < p < 0.373

(0.227 , 0.373)