Optimal Sample Size for Testing Raisin Content in Buns

  • Thread starter Thread starter superwolf
  • Start date Start date
superwolf
Messages
179
Reaction score
0
If the average number of raisins in a randomly chosen bun is 9 with a variance of 9, how many buns must be tested if a test with a significance level of 0.05 with 90% probability is going to reveal than the number of raisins is less than 10?

ATTEMPT:

<br /> n = \frac{(z_{\alpha} + z_{\beta})^2 \sigma^2}{\delta^2} = \frac{(1.645+1.28)^2 \cdot 9}{1^2} = 77.0006

So, at least 78 buns.

Correct answer. At least 82 buns.

What's wrong?
 
Physics news on Phys.org
Help us out here. What test are you using? It looks vaguely like something to do with the F statistic, but I don't have my statistics references with me. What do z_alpha and z_beta represent, and how did you get them?
 
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...

Similar threads

Back
Top