Question 14.43

14.43 Pooling variances.

An experiment was run to compare four groups. The sample sizes were 30, 32, 150, and 33, and the corresponding estimated standard deviations were 25, 22, 13, and 23.

  1. Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer.
  2. Give the values of the variances for the four groups.
  3. Find the pooled variance.
  4. What is the value of the pooled standard deviation?
  5. Explain why your answer in part (c) is much closer to the standard deviation for the third group than to any of the other standard deviations.

14.43

(a) Yes, the largest is less than twice the smallest ; . (b) 625, 484, 169, 529. (c) . (d) . (e) The third group has the largest sample size and will influence or weight the pooled standard deviation more.