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MattMurdock
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Homework Statement
I'm working on a problem in Design and Analysis of Experiments by Dean and Voss. It's Chapter 10 question 11 part c.
We have an experiment with 2 treatment factors (each with three levels) and 1 blocking factor (with four levels. It's a randomized complete block design so only one experimental unit per treatment/block combination:
[tex]y_{hij} = \mu + \theta_h + \alpha_i + \beta_j + (\alpha\beta)_{ij} + \epsilon_{hij}[/tex]
where [itex]\theta_h[/itex] refers to the [itex]h^{th}[/itex] block effect and [itex]\alpha_i[/itex] refers to the effect of factor A, [itex]\beta_j[/itex] refers to the effect of factor B and [itex](\alpha\beta)_{ij}[/itex] refers to the interaction between the 2.
The experimenters want Scheffe 95% confidence intervals for normalized contrasts in the main effects of each factor to be no wider than 10. A pilot experiment was run to give an estimate for MSE equal to 670. How many subjects are needed?
Homework Equations
The Attempt at a Solution
The width of a Scheffe interval is defined to be [itex]2\sqrt{(3−1)F_{3−1,8(b−1),0.05}} \sqrt{MSE}[/itex]
Where [itex]8(b−1)[/itex] is the degrees of freedom of SSE and MSE is the variance of the contrasts since they are normalized.
If this is to be less than or equal to 10 then [itex]F_{2,8(b−1),0.05} \leq \frac{25}{670∗2}=0.0186567[/itex]
My problem is that I don't think I can possibly make this inequality work because the F critical values never go below 3 for a numerator degree of freedom equal to 2. I was wondering if anyone could shed some light on this for me. Am I making a mistake or is there something wrong with the question? Thank you
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