Question

A survey asked subjects if they would be willing to accept cuts in their standard of living to protect the environment, 344 of 1170 subjects said yes.

a. Estimate the population proportion who would answer yes.

b. Find the margin of error for a 95% confidence interval for this estimate.

c. Find a 95% confidence interval for that proportion.

d. Interpret the confidence interval in context.

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 344 / 1170 = 0.294

1 - = 1 - 0.294 = 0.706

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.294 * 0.706) / 1170)

= 0.013

c) A 95% confidence interval for population proportion p is ,

± E  

0.294 ± 0.013

(0.281 , 0.307)

d) We are 95% confident that the true proportion of living to protect the environment between 0.281 and 0.307