Sample Size = n = 1200
Number of people who are willing to pay higher = x = 708
Proportion of people who are willing to pay higher = p = [tex] \frac{708}{1200}= \frac{59}{100}=0.59 [/tex]
Confidence Level = 99%
Z Value = z = 2.58
The confidence interval about a population proportion can be calculated as:
[tex](p-z \sqrt{ \frac{p(1-p)}{n} }, p+z \sqrt{ \frac{p(1-p)}{n} })[/tex]
Using the values, we get:
[tex](0.59-2.58 \sqrt{ \frac{0.59(0.41)}{1200} } ,0.59+2.58 \sqrt{ \frac{0.59(0.41)}{1200} }) \\ \\
(0.553,0.627)[/tex]
Thus, at 99% confidence level, the estimated proportion of people willing to pay higher prices for gas in order to protect the environment lies between 0.553 and 0.627.
