12.3 Computing the pooled standard deviation. An experiment was run to compare three timed-release fertilizers in terms of plant growth. The sample sizes were 23, 21, and 27 plants, and the corresponding estimated standard deviations were 4, 5, and 7 centimeters.

(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?