Answer:
The point estimate of this proportion is ![\pi = 0.5857](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.5857)
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
For this problem, we have that:
![n = 1255, \pi = \frac{735}{1255} = 0.5857](https://tex.z-dn.net/?f=n%20%3D%201255%2C%20%5Cpi%20%3D%20%5Cfrac%7B735%7D%7B1255%7D%20%3D%200.5857)
The point estimate of this proportion is ![\pi = 0.5857](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.5857)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.5857%20-%201.96%5Csqrt%7B%5Cfrac%7B0.5857%2A0.4143%7D%7B1255%7D%7D%20%3D%200.5584)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.5857%20%2B%201.96%5Csqrt%7B%5Cfrac%7B0.5857%2A0.4143%7D%7B1255%7D%7D%20%3D%200.6130)
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).