Refer to Problem 3-26.

(a) How would your answer change if a reasonable estimate of the experimental error variance were σ² = 36?

(b) How would your answer change if a reasonable estimate of the experimental error variance were σ² = 49?

(c) Can you draw any conclusions about the sensitivity of your answer in this particular situation about how your estimate of σ affects the decision about sample size?

(d) Can you make any recommendations about how we should use this general approach to choosing n in practice?

Problem 3-26.

Suppose that four normal populations have means of µ₁ = 50, µ₂ = 60, µ₃ = 50, and µ₄ = 60. How many observations should be taken from each population so that the probability of rejecting the null hypothesis of equal population means is at least 0.90? Assume that α = 0.05 and that a reasonable estimate of the error variance is σ² = 25.