Question

Is the environment a major issue with Americans? To answer that question, a researcher conducts a survey of 1255 randomly selected Americans. Suppose 738 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?

Answer 1

ANSWER::

let p represent population proportion

and p^ represent sample proportion

and n represent sample size

we have p^ =x/n=738/1255=0.5880

since sample size is large use z multiplier

z for 95% is 1.96

95% confidence interval for population proportion is given by:

0.5880±1.96sqrt(0.5880(1-0.5880)/1255

0.5880 ±0.0272

0.5880-0.0272<p<0.5880+0.0272

0.5608<p<0.6125

0.561<p<0.615

lower boundary=0.561

=0.561*100

=56.1%

upper boundary=0.615

=0.615*100

=61.5%

we are 95% confident that the true population proprtion lies in between 56.1% and 61.5%

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