Question

An experiment is conducted to determine whether there is a differnce among the mean increases in...

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 19 21 25 19 10
Plant 2 17 21 22 12 11
Plant 3 15 16 25 18 12
Plant 4 10 25 24 1616 13
Mean 15.25 20.75 24 16.25 11.5
Standard Dev. 3.8622 3.6856 1.4142 3.0957 1.2910

It is also given that the overall mean = 17.55.

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

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given:

The total number of treatments (k) is 5.

The total number of experimental units (N) is 20.

The overall mean (x̄) is 17.55

The provided data is,

Pants

A

B

C

D

E

1

19

21

25

19

10

2

17

21

22

12

11

3

15

16

25

18

12

4

10

25

24

16

13

ni

4

4

4

4

4

x̄i

15.25

20.75

24

16.25

11.5

si

3.8622

3.6856

1.4142

3.0957

1.291

(a):

(b):

(c):

(d):

(e):

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