Calculating the pooled standard deviation. An experiment was run to compare three groups. The sample sizes were 29, 32, and 121, and the corresponding estimated standard deviations were 37, 28, and 42.
(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 three 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 two standard deviations.