An experiment is conducted to determine whether there is a differnce among the m

Question

An experiment is conducted to determine whether there is a differnce 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.

A B C D E
Plant 1 9 26 23 12 10
Plant 2 19 19 21 16 11
Plant 3 16 20 23 19 15
Plant 4 10 21 21 13 14
Mean 13.5 21.5 22 15 12.5
Standard Dev. 4.7958 3.1091 1.1547 3.1623 2.3805

It is also given that the overall mean = 16.9.

Compute the following:
(a) SSTR=  
(b) SSE =  
(c) MSTR =  
(d) MSE =  
(e) F

Explanation / Answer

from abvoe SSTR =326.80

SSE =149.00

MSTR =81.70

MSE =9.93

F =8.225

Grade ni x?i S2i ni*(Xi-Xgrand)2 (ni-1)*S2i A 4 13.5000 22.9997 46.240 69.00 B 4 21.5000 9.6665 84.640 29.00 C 4 22.0000 1.3333 104.040 4.00 D 4 15.0000 10.0001 14.440 30.00 E 4 12.5000 5.6668 77.440 17.00 16.90 326.800 149.00 SSTr SSE Source of variation SS df MS F treatment 326.800 4 81.700 8.225 error 148.999 15 9.933 total 475.799 19

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