Statistics - Tests of Hypotheses

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Homework Statement


Consider N(μ, σ2=40) distribution. To test H0:=32 against H1:μ>32, we reject H0if the sample mean \overline{X}≥c. Find the sample size n and the constant c such that OC(μ=32)=0.90 AND OC(μ=35)=0.15.


Homework Equations



What I don't know

The Attempt at a Solution



Can't figure out how to do this one.
 
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XodoX said:

Homework Statement


Consider N(μ, σ2=40) distribution. To test H0:=32 against H1:μ>32, we reject H0if the sample mean \overline{X}≥c. Find the sample size n and the constant c such that OC(μ=32)=0.90 AND OC(μ=35)=0.15.


Homework Equations



What I don't know

The Attempt at a Solution



Can't figure out how to do this one.

Show your work. Tell us why you cannot just use the material from the textbook or the course notes to get started with this problem.

RGV
 
Ray Vickson said:
Show your work. Tell us why you cannot just use the material from the textbook or the course notes to get started with this problem.

RGV

What work? I do not have anything. "What I don't know" under relevant equation means I don't know which equation to use, because I do not find one that would work here. If I had found something, I would not have asked.
 
Last edited:
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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