Sample Size Determination. In the single-factor completely

Chapter 13, Problem 77MEE

(choose chapter or problem)

Sample Size Determination. In the single-factor completely randomized design, the accuracy of a100\((1-\alpha) \%\) confidence interval on the difference in any two treatment

means is

\(t_{\alpha / 2, a(n-1)} \sqrt{2 M S_{E} / n}\)

(a) Show that if A is the desired accuracy of the interval,

the sample size required is

\(n=\frac{2 F_{\alpha / 2,1, a(n-1)} M S_{E}}{A^{2}}\)

(b) Suppose that in comparing \(a=5\)  means you have a preliminary estimate of \(\sigma^{2}\) of 4. If you want the \(95 \%\) confidence interval on the difference in means to have an accuracy of 2, how many replicates should you use?

 

Equation Transcription:

 

 

   

   

       

Text Transcription:

(1-\alpha) \%

\(t_\alpha / 2, a(n-1)} \sqrt 2 M S_E / n)

\(n=2 F_\alpha / 2,1, a(n-1)} M S_E A^2)

a=5  

\sigma^2

95%