Suppose that four normal populations have means of

????1 = 50, ????2 = 60, ????3 = 50, and ????4 = 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 ???? = 0.05 and that a reasonable estimate of the error variance is ????

2 = 25.

3.53 Refer to Problem 3.52.

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

????

2 = 36?

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

2 = 49?

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

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