An experiment is conducted to determine whether there is a difference among the

Question

An experiment is conducted to determine whether there is a difference among the mean increases in growth produced by five strains (A, B, C, D and E)of growth hormones for plants. The experimental material consists of 20 cuttings of a shrub (all of equal weight), with four cuttings randomly assigned to each of the five different strains. The increases in weight for each cutting along with the sample mean and sample standard deviation of each group are given in the table below. It is also given that the overall mean = 17.4. Compute the following: (a) SSTR = (b) SSE = (c) MSTR = (d) MSE = (e) F =

Explanation / Answer

a)SSTR=503.80

b)SSE=163

c)MSTR =SSTR/(k-1) =125.95

d) MSE =SSE/(N-k)=163/15=10.867

e)F=MSTR/MSE=11.590

i ni Xi Si^2 ni*(Xi-mean)^2 (n1-1)*Si^2 A 1 4 14.75 10.916 28.090 32.7492 B 2 4 22.75 14.917 114.490 44.7498 C 3 4 23.75 3.583 161.290 10.7503 D 4 4 15 14.667 23.040 43.9998 E 5 4 10.75 10.250 176.890 30.7507 mean 17.400 503.800 163.000 SSG SSE Source of variation SS df MS F P value F crit treatment 503.800 4 125.950 11.590 0.0002 3.0556 error 163.000 15 10.867 total 666.800 19

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