Question

In 2015 as part of the General Social Survey, 1220 randomly selected American adults responded to this question:

“Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?”

Of the respondents, 492 replied that America is doing about the right amount. What is the 95% confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment.

1. (0.38, 0.426)
2. (0.367, 0.439)
3. (0.376, 0.431)
4. (0.389, 0.417)

Answer 1

Solution :

Given that,

n = 1220

x = 492

Point estimate = sample proportion = = x / n = 492/1220=0.403

1 -   = 1- 0.403 =0.597

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.403*0.597) / 1220)

= 0.0275

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.403-0.0275 < p <0.403+ 0.0275

0.376< p < 0.431

The 95% confidence interval for the population proportion p is :0.376, 0.431