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Science Forum Index » Statistics - Math Forum » Solving nonlinear system numerically?
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| Walkman |
 Posted: Sat Apr 05, 2008 6:56 pm |
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Guest
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I've got stuck with a problem in Hogg(8.1.7, "Introduction to
mathematical statistics 6E)
This is on "Test"
n random samples be iid with f(x;theta) = N(theta,100)
To find n and c such that a best critical region suffices with simple
hypothesis H0: theta =75 vs. H1: theta = 78
Under H0 P(x_bar >= c) = .05
Under H1 P(x_bar >= c) = .9
As far as I knew, the problem can be solved numerically, I tried to
solve it using Mathematica; still did not finish.
I need someone who can inspire me on this problem or solve it
practically using some math-computational program(e.g. mathematica, R)
I don't know that I fully explained the problem itselt to you. If you
have any problem in solving this, please let me know.
Thank U for reading.
Have a nice day~
Walkman. |
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| Paul Rubin |
| Posted: Sun Apr 06, 2008 8:49 am |
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Guest
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Walkman wrote:
Quote: I've got stuck with a problem in Hogg(8.1.7, "Introduction to
mathematical statistics 6E)
This is on "Test"
n random samples be iid with f(x;theta) = N(theta,100)
To find n and c such that a best critical region suffices with simple
hypothesis H0: theta =75 vs. H1: theta = 78
Under H0 P(x_bar >= c) = .05
Under H1 P(x_bar >= c) = .9
As far as I knew, the problem can be solved numerically, I tried to
solve it using Mathematica; still did not finish.
I need someone who can inspire me on this problem or solve it
practically using some math-computational program(e.g. mathematica, R)
I don't know that I fully explained the problem itselt to you. If you
have any problem in solving this, please let me know.
Thank U for reading.
Have a nice day~
Walkman.
Use the inverse CDF (available in Mathematica, R, Minitab, Excel, ...)
to get to an easily solved system of two equations in two unknowns
(which you can then solve with a calculator).
Incidentally, the exact solution will yield a non-integer value for n.
You can round it, but then the probabilities will be only approximately
accurate.
/Paul |
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