Question

When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the​ environment, 370 of 1150 subjects said yes.

(a) Find the point estimate of the proportion of the population who would answer yes.

(b) Find the margin of error for a​ 95% confidence interval.

(c) Construct the​ 95% confidence interval for the population proportion. What do the numbers in this interval​ represent?

Answer 1

Solution:

a) point estimate of a sample proportion is obtained using the formula;

$\widehat{p}=\frac{x}{n}$

Where $\widehat{p}= point estimate$

x = sample size

n = population size

$\widehat{p}= \frac{370}{1150}$

$\widehat{p}= 0.3217$

Hence, the point estimate of the proportion of the population is 0.3217

b) The desired margin of error is the calculated using the point estimate value as follows:

ME= 2* p(1 p) n

$\widehat{p}= 0.3217$

$ME= 1.96*\sqrt{\frac{0.3217(1-0.3217)}{1150}}$

ME = 0.02621

c) G a confidence level of 95%, the confidence interval can be calculated as:

$CI= \widehat{p}+- ME$

CI = 0.3217 +- 0.02621

CI= (0.29549,0.34791)

Hence, the confidence interval at 95% confidence level is

0.29549 < p < 0.34791