Calculating the pooled standard deviation. An experiment was run to compare four groups. The sample sizes were 25, 28, 150, and 21, and the corresponding estimated standard deviations were 42, 38, 20, and 45.
(a) Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer.
(b) Give the values of the variances for the four groups.
(c) Find the pooled variance.
(d) What is the value of the pooled standard deviation?
(e) Explain why your answer in part (d) is much closer to the standard deviation for the third group than to any of the other standard deviations.