In: Statistics and Probability
Is the environment a major issue with Americans? To answer that
question, a researcher conducts a survey of 1255 randomly selected
Americans. Suppose 730 of the sampled people replied that the
environment is a major issue with them. Construct a 95% confidence
interval to estimate the proportion of Americans who feel that the
environment is a major issue with them. What is the point estimate
of this proportion?
(Round the intermediate values to 3 decimal places.
Round your answer to 3 decimal places.)
enter the lower limit of the confidence interval ≤ p ≤
enter the upper limit of the confidence interval
The point estimate is enter the point estimate .
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 730 / 1255 = 0.582
1 -
= 1 - 0.582 = 0.418
Z/2
= 1.96
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.96 * (((0.582
* 0.418) / 1255)
= 0.027
A 95% confidence interval for population proportion p is ,
- E
p
+ E
0.582 - 0.027
p
0.582 + 0.027
0.555
p
0.609
The lower limit of the confidence interval 0.555 ≤ p ≤ 0.609 enter the upper limit of the confidence interval