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.

Also added that overall mean = 15.75.

Compute the following quanitites:

(a) Sum of Squares of Treatment = SSTR=
(b) Sum of Squares of Error = SSE =  
(c) Mean Square of Treatment = MSTR =
(d) Mean Square Error= MSE =
(e) F statistic=

Plant 1 Plant 2 Plant 3 Plant 4 1516 23 1310 1123 21166 14192416 10 9 20 20 15 14 Mean 12.2519.5221510 Standard Dev. 2.7538 2.88681.82571.41423.2660

Explanation / Answer

from above:

a)  Sum of Squares of Treatment = SSTR= =396

b) Sum of Squares of Error = SSE = 95.751

c) Mean Square of Treatment = MSTR = 198

d) Mean Square Error= MSE = 5.632

e)  F statistic= 35.154

i ni xi S2i ni*(Xi-Xgrand)2 (ni-1)*S2i A 4 12.25 7.583 49.000 22.750 B 4 19.5 8.334 56.250 25.001 C 4 22 3.333 156.250 10.000 D 4 15 2.000 2.250 6.000 E 4 10 10.667 132.250 32.000 Grand mean=Xgrand=xi*ni/ni= 15.750 396.000 95.751 SSG SSE Source of variation SS df MS F P value F crit treatment 396.000 2 198.000 35.154 0.0000 3.5915 error 95.751 17 5.632 total 491.751 19

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