Question

The removal of ammoniacal nitrogen is an important aspect of treatment of leachate at landfill sites. The rate of removal (in percent per day) is recorded for several days for each of several treatment methods. The results are presented in the following table.

Treatment	Rate of Removal
A	5.21	4.65
B	5.59	2.69	7.57	5.16
C	6.24	5.94	6.41
D	6.85	9.18	4.94
E	3.6	2.9	4.1	3.4

Construct an ANOVA table.

Source	DF	SS	MS	F	P
Treatment					(Click to select)P < 0.001P > 0.100.001 < P < 0.010.05 < P < 0.100.01 < P < 0.05
Error
Total

Answer 1

Solution:

Here, we have to construct the ANOVA table for the given data with five treatments. Descriptive statistics and one way ANOVA table by using excel is given as below:

Null hypothesis: H₀: There is no significant difference in average rate of removal for five treatments.

Alternative hypothesis: H_a: There is a significant difference in the average rate of removal for five treatments.

Descriptive Statistics

Groups	Count	Sum	Average	Variance
A	2	9.86	4.93	0.1568
B	4	21.01	5.2525	4.019892
C	3	18.59	6.196667	0.056633
D	3	20.97	6.99	4.5091
E	4	14	3.5	0.246667

ANOVA
Source	SS	df	MS	F	P-value
Treatment	24.2146	4	6.053651	3.014774	0.05 < P < 0.10
Error	22.08794	11	2.007995
Total	46.30254	15

The exact P-value for this ANOVA table is given as 0.066137123 which is greater than alpha value 0.05, so we do not reject the null hypothesis at 5% level of significance.

There is insufficient evidence at 5% level of significance to conclude that there is a significant difference in the average rate of removal for five treatments.