Hitaro9
  • Hitaro9
Statistics - Confidence Interval, How did they get these answers?
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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Hitaro9
  • Hitaro9
http://puu.sh/lLTjm/1c94bf4dd3.png
amistre64
  • amistre64
what do you get for Z and mu?
Hitaro9
  • Hitaro9
Sorry. 3.98 would be the sample mean. For Z I would assume we'd be using the normal confidence interval for 95% of 1.96

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amistre64
  • amistre64
im getting 3.483 as a mean ... but most of that was adding in my head
Hitaro9
  • Hitaro9
The distribution is poisson though right? So the confidence interval is going to be asymmetric.
Hitaro9
  • Hitaro9
Cause if you take the answers they've given it's not centered around either of our answers for the mean
amistre64
  • amistre64
4.015 yeah ... i spose we would work it so that we have a left tail of 5/2 and a right tail of 5/2
amistre64
  • amistre64
i spose we have a calculator for this? or tables?
Hitaro9
  • Hitaro9
Yeah, I have an appendix of tables and calculator access is fine. Is there a specific table you wanted me to check?
amistre64
  • amistre64
i dont have much experience in poisson, but im sure the table is one with ns and percentages .. similar to a t-distribution table
Hitaro9
  • Hitaro9
Poisson is asymmetric, this is what it'd look like for 3.98 : http://puu.sh/lLXfR/bcf3692e4b.png So it'd make sense that it'd be centered around 2.015 for a confidence interval
amistre64
  • amistre64
how do we determine say the value of X, such that 2.5% is in a left tail?
Hitaro9
  • Hitaro9
I'm not sure. That's where I'm having trouble
amistre64
  • amistre64
http://onbiostatistics.blogspot.com/2014/03/computing-confidence-interval-for.html this would suggest that we simply do a conventional interval method, using the standard error or whatever its called to be sqrt(u/n)
Hitaro9
  • Hitaro9
Okay. I've been using the normal approximation thus far, and that's giving me the wrong values. I'll see if I can follow their method for the exact values
Hitaro9
  • Hitaro9
So according to this table (our provided table doesn't go up to n=50) the value we should be using is 32.357 I think? Am I reading this correctly?
Hitaro9
  • Hitaro9
Wait nevermind I'm dumb
Hitaro9
  • Hitaro9
So we need to enter in the custom value of 3.98 for the formula for chi squared?
Hitaro9
  • Hitaro9
http://puu.sh/lLY9r/271ebc29d4.png Trying this thing.
amistre64
  • amistre64
im getting a mean of 3.98 3.98 - 1.96sqrt(3.98/60) = 3.475 3.98 + 1.96sqrt(3.98/60) = 4.485 which of course is not what the solutions say it is .... so they must have gone a different route eh. and i cant really make sense of that last link you posted.
Hitaro9
  • Hitaro9
On the link you posted, it says there are two ways to do it. The normal approximation and the "EXACT method"
Hitaro9
  • Hitaro9
The exact method relies on chi squared: (qchisq(α/2, 2*x)/2, qchisq(1-α/2, 2*(x+1))/2 )
Hitaro9
  • Hitaro9
And that link I posted in the chi squared formula I think? I may be looking at the wrong thing.
Hitaro9
  • Hitaro9
Whatever the answer is, its definitely not going to be of the form 3.98+- something right? Otherwise the interval would be centered around 3.98
amistre64
  • amistre64
correct, that method is approximation, im reading up in a chi^2 method
amistre64
  • amistre64
but your hint suggests the approximation method if im reading it right
Hitaro9
  • Hitaro9
Right. I think the hint is just misleading.
Hitaro9
  • Hitaro9
Unless there's some easy way to derive mu from x bar.
Hitaro9
  • Hitaro9
I don't know enough about poisson though, and google searches didn't find anything
Hitaro9
  • Hitaro9
So this website's calculator got fairly close: http://calculator.tutorvista.com/confidence-interval-calculator.html http://puu.sh/lLZsZ/6ee99f02c1.png Close enough that it may be me entering something in wrong
amistre64
  • amistre64
without having gone thru your materials, id have to say that i am just too inexperienced to determine a suitable solution process at the moment.
Hitaro9
  • Hitaro9
Would it help if I provided the associated chapter? I believe its on google books
amistre64
  • amistre64
it would be useful, but i cant guarentee anything from it
Hitaro9
  • Hitaro9
Actually having some trouble finding it, sorry. Alright, thank you for your help either way. Helping me think through the problem has been help enough. Thank you.
amistre64
  • amistre64
the best of luck to you :)

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