Answer: = [tex]0.444\pm 0.111[/tex]
Step-by-step explanation:
The confidence interval for population proportion(p) is given by :-
[tex]\hat{p}-E<p<\hat{p}+E[/tex] (1)
It is also written as : [tex]\hat{p}\pm E[/tex] (*)
The given confidence interval for population proportion :
[tex]0.333<p<0.555[/tex] (2)
Comparing (1) and (2) , we get
Lower limit = [tex]\hat{p}-E=0.333[/tex] (3)
Upper limit = [tex]\hat{p}+E=0.555[/tex] (4)
Adding (3) and (4) , we get
[tex]2\hat{p}=0.888\\\Rightarrow\ \hat{p}=\dfrac{0.888}{2}=0.444[/tex]
Put value of [tex]\hat{p}=0.444[/tex] in (2) , we get
[tex]0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111[/tex]
Put values of [tex]\hat{p}=0.444[/tex] and E= 0.111 in (*) , we get
Required form = [tex]0.444\pm 0.111[/tex]
