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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