How do I rewrite the confidence interval (0.0268, 0.133) in the form of hatp - E < p < hatp + E?

1 Answer
Geoff K.
Dec 7, 2016

0.0799-0.0531< p < 0.0799+0.0531.

Explanation:

If I understand correctly, we simply need to take the confidence bounds (0.0268, 0.133) and convert them to a "central value" hatp, plus/minus an error margin E.

hatp will be halfway between our lower- and upper-bound, and so we take the average of the two bounds:

hatp=(0.0268+0.133)/2=0.1598/2=0.0799

The error margin E will just be the distance between this hatp value and one of the original bounds:

E=abs(hatp-0.0268) or E=abs(hatp-0.133)
color(white)E=abs(0.0799-0.0268)=abs(0.0799-0.133)
color(white)E=abs(0.0531)color(white)(XXXXiii)=abs(-0.0531)
color(white)E=0.0531

So in hatp-E < p < hatp + E form, our confidence interval is

0.0799-0.0531< p < 0.0799+0.0531
or
p in (0.0799+-0.0531).

I hope this is the answer you're looking for!

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