Question

In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. Calculate and interpret a 95% confidence interval for the proportion of all U.S. adults in 5 April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.

Answer 1

Answer:  95% confidence interval would be (0.449, 0.511)

Step-by-step explanation:

Since we have given that

n = 1022

p = 48% = 0.48

We need to find the 95% confidence interval first.

z = 1.96

Margin of error would be

$z\sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.48\times 0.52}{1022}}\\\\=0.031$

95% confidence interval would be

$p\pm 0.031\\\\=(0.48-0.031,0.48+0.031)\\\\=(0.449,0.511)$

It means true proportion who felt that economic growth is more important than protecting the environment is within 0.449 and 0.511 using 95% confidence.