Question

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.
(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 either of the other two standard deviations.

Answer 1

Given information:

(a)

let us fid the ratio of smallest and largest standard deviation.

Since it is less than 2 so we can assume that populaion variances are equal.

(b)

(c)

The pooled variance is

(d)

The pooled standard deviation is

(e)

Becuase the standard deviation other two groups are much smaller than the standard deviation of third group.