Question

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

Answer 1

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

Answer 2

what do you get for Z and mu?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

i dont have much experience in poisson, but im sure the table is one with ns and percentages .. similar to a t-distribution table

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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)

Answer 15

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

Answer 16

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?

Answer 17

Wait nevermind I'm dumb

Answer 18

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

Answer 19

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

Answer 20

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.

Answer 21

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

Answer 22

The exact method relies on chi squared:


(qchisq(α/2, 2*x)/2, qchisq(1-α/2, 2*(x+1))/2 )

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

Right. I think the hint is just misleading.

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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.

Answer 32

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

Answer 33

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

Answer 34

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.

Answer 35

the best of luck to you :)