Statistics - Confidence Interval, How did they get these answers?

- Hitaro9

Statistics - Confidence Interval, How did they get these answers?

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- Hitaro9

http://puu.sh/lLTjm/1c94bf4dd3.png

- amistre64

what do you get for Z and mu?

- 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

im getting 3.483 as a mean ... but most of that was adding in my head

- Hitaro9

The distribution is poisson though right? So the confidence interval is going to be asymmetric.

- Hitaro9

Cause if you take the answers they've given it's not centered around either of our answers for the mean

- 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

i spose we have a calculator for this? or tables?

- Hitaro9

Yeah, I have an appendix of tables and calculator access is fine. Is there a specific table you wanted me to check?

- 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

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

how do we determine say the value of X, such that 2.5% is in a left tail?

- Hitaro9

I'm not sure. That's where I'm having trouble

- 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

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

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

Wait nevermind I'm dumb

- Hitaro9

So we need to enter in the custom value of 3.98 for the formula for chi squared?

- Hitaro9

http://puu.sh/lLY9r/271ebc29d4.png Trying this thing.

- 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

On the link you posted, it says there are two ways to do it. The normal approximation and the "EXACT method"

- Hitaro9

The exact method relies on chi squared:
(qchisq(α/2, 2*x)/2, qchisq(1-α/2, 2*(x+1))/2 )

- Hitaro9

And that link I posted in the chi squared formula I think? I may be looking at the wrong thing.

- 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

correct, that method is approximation, im reading up in a chi^2 method

- amistre64

but your hint suggests the approximation method if im reading it right

- Hitaro9

Right. I think the hint is just misleading.

- Hitaro9

Unless there's some easy way to derive mu from x bar.

- Hitaro9

I don't know enough about poisson though, and google searches didn't find anything

- 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

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

Would it help if I provided the associated chapter? I believe its on google books

- amistre64

it would be useful, but i cant guarentee anything from it

- 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

the best of luck to you :)

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