Formula to find the confidence interval for population proportion (p) is given by :-
, where z* = Critical value.
= Sample proportion.
SE= Standard error.
Let p be the true population proportionof U.S. adults who live with one or more chronic conditions.
As per given , we have
SE=0.012
By z-table , the critical value for 95% confidence interval : z* = 1.96
Now , a 95% confidence interval for the proportion of U.S. adults who live with one or more chronic conditions.:
Hence, a 95% confidence interval for the proportion of U.S. adults who live with one or more chronic conditions.
Interpretation : Pew Research Foundation can be 95% confident that the true population proportion (p) of U.S. adults who live with one or more chronic conditions lies between 0.42648 and 0.47352 .