Question

g In 2010 as part of the General Social Survey, 1295 randomly selected American adults responded to this question: "Some countries are doing more to protect the environment than other countries are. In general, do you think that America is doing more than enough, about the right amount, or too little?"

Answer 1

0.339 , 0.391

Explanation:

n = 1295

x = 473

\hat p = x / n = 473 / 1295 = 0.365

1 - \hat p = 1 - 0.365 = 0.635

At 95% confidence level the z is ,

\alpha = 1 - 95% = 1 - 0.95 = 0.05

\alpha / 2 = 0.05 / 2 = 0.025

Z\alpha/2 = Z0.025 = 1.96

Margin of error = E = Z\alpha / 2 * \sqrt((\hat p * (1 - \hat p)) / n)

= 1.96 * (\sqrt((0.365 * 0.635) / 1295)

= 0.026

A 95% confidence interval for population proportion p is ,

\hat p - E < P <\hat p + E

0.365 - 0.026 < p < 0.365 + 0.026

0.339 < p < 0.391

(0.339 , 0.391)