Computing the pooled standard deviation. An experiment was run to compare three timed-release fertilizers in terms of plant growth. The sample sizes were 25, 18, and 28, 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?