12.16 Calculating the pooled standard deviation. An experiment was run to compare three groups. The sample sizes were 28, 33, and 102, and the corresponding estimated standard deviations were 2.7, 2.6, and 4.8.

  1. (a) Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer.

  2. (b) Give the values of the variances for the three groups.

  3. (c) Find the pooled variance.

  4. (d) What is the value of the pooled standard deviation?

  5. (e) Explain why your answer in part (d) is much closer to the standard deviation for the third group than to either of the other two standard deviations.