Question

compare the concentration (in ppm) of a particular item in lake water

Construct a nova table and determine if the concentrations differ between the lakes

lake1	lake2	lake3
12.7	8.3	20.3
9.2	17.2	16.6
10.9	19.1	22.7
8.9	10.3	25.2
6.4		19.9

Answer 1

The following table is obtained:

	Lake 1	Lake 2	Lake 3
	12.7	8.3	20.3
	9.2	17.2	16.6
	10.9	19.1	22.7
	8.9	10.3	25.2
	6.4		19.9
Sum =	48.1	54.9	104.7
Average =	9.62	13.725	20.94
	484.91	835.63	2233.99
St. Dev. =	2.355	5.232	3.224
SS =	22.188	82.1275	41.572
n =	5	4	5

Number of treatment, k = 3

Total size, N = 14

Grand mean =

Also, the sum of squared values is

Based on the above calculations, the total sum of squares is computed as follows

The within sum of squares is computed as shown in the calculation below:

The between sum of squares is computed directly as shown in the calculation below:

Source of Variation	SS	df	MS	F
Between Groups	327.2646	2	327.2646/2 = 163.6323	12.338
Within Groups	145.8875	11	145.8875/11 = 13.2625
Total	473.1521	13

Null and Alternative hypothesis:

H1: At least one mean is different.

Test statistic:

F = 12.338

p-value = 0.0015

As p =0.0015 < we, reject the null hypothesis.

There is enough evidence to claim that at least one mean is different.