Question

Express the confidence interval 0.333 less than p less than 0.555 in the form Modifying Above p with caret plus or minus Upper E. Modifying Above p with caret plus or minus Upper E equals nothing plus or minus nothing

Answer 1

Answer: = $0.444\pm 0.111$

Step-by-step explanation:

The confidence interval for population proportion(p) is given by :-

$\hat{p}-E$  (1)

It is also written as : $\hat{p}\pm E$         (*)

The given confidence interval for population proportion :

$0.333$ (2)

Comparing (1) and (2) , we get

Lower limit = $\hat{p}-E=0.333$ (3)

Upper limit = $\hat{p}+E=0.555$  (4)

Adding (3) and (4) , we get

$2\hat{p}=0.888\\\Rightarrow\ \hat{p}=\dfrac{0.888}{2}=0.444$

Put value of $\hat{p}=0.444$ in (2) , we get

$0.444+E=0.555\\\\\Rightarrow\ E=0.555-0.444=0.111$

Put values of $\hat{p}=0.444$  and E= 0.111 in (*) , we get

Required form = $0.444\pm 0.111$