Question

In 2006, the General Social Survey asked, "In the past 12 months, have you experienced back pain?." For this question, 475 people said that they did out of 1723 randomly selected people. What is the 95% confidence interval for the proportion of all Americans that have experienced back pain in the past 12 months?

Answer 1

Answer:

The 95% confidence interval for the percentage of  all Americans that have experienced back pain in the last 12 months is 0.27 (27%), plus or minus 0.0209 (2.09%). Or, between 29.09% and 24.91% of all Americans have experienced back pain in the past 12 months.

Explanation:

The formula for a Confidence Interval (CI) for a population proportion is:

p±z$\sqrt[2]{p(1-p)/n}$

where

p= Population proportion

n= sample size

z= appropriate value from the standard normal distribution for the desired confidence level

p= 475/1723

p=0.27

n=1723

z=1.96 (for a 95% confidence level)

$1.96\sqrt[2]{(0.27)(0.73)/1723}$ = 0.0209

so we have

CI= 0.27 ± 0.0209