Question

Table Q4 shows the means for the removal reduction of chemical oxygen demand (COD) in wastewater by three different treatment methods. By using One-Way Analysis of Variance (ANOVA), test the validity of hypothesis that there are no differences among the reduction percentage by the treatment method at significance level of 0.05 (a 0.05) (25 marks)

need help

Answer 1

Here we have data:

Treatment 1	Treatment 2	Treatment 3
40	50	60
40	60	70
50	60	90
60	70	90
80	80	80
90

Here we are using excel for calculation:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
40	5	320	64	430
50	4	270	67.5	91.6667
60	4	330	82.5	91.6667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	822.3077	2	411.1538	1.8113	0.2132	4.1028
Within Groups	2270	10	227
Total	3092.3077	12

Hypothesis:

H_o; μ₁ = μ₂ = μ₃

H_a; At least one mean is difference from others.

Test statistics :

F = 1.8113

Critical value:

F_c = 4.1028

P-value = 0.2132

Alpha value = 0.05

Fail to reject the null hypothesis

Here we have not sufficient evidence to reject the null hypothesis F-observed value is less than F-critical value and P-value is grater than alpha value.

We can say that there is no difference in three treatment method.