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

Sample Size Determination. In the single-factor completely randomized design, the accuracy of a100(1 ˆ’ α)% confidence interval on the difference in any two treatment means is t_{a/2,a(n€“1)}ˆš2MS_E/ n.

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

(b) Suppose that in comparing a = 5 means you have a preliminary estimate of σ² 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?

2Falz1de-1) MSE A?