Three drinking water treatment methods are being tested on a standardized water

Question

Three drinking water treatment methods are being tested on a standardized water sample with a known contaminant level. Post-treatment contaminant levels (i.e. the response variable) are listed in the table below. Five water samples were tested for each treatment method. Conduct an ANOVA on these data.

Contaminant levels (mg/L)

Treatment Method 1: 9.12 9.88 9.56 9.53 8.25

Treatment Method 2: 10.51, 11.23, 10.96, 11.97, 12.34

Treatment Method 3: 9.10, 9.62, 12.37, 9.21, 9.42

A. Hypotheses:

B. Test statistic:

C. P-value:

D. Significance level:

E. Interpretation:

F. If the results are significant, complete post hoc comparisons of the groups using the Bonferroni method. Regardless of the need for post hoc comparisons, explain WHY post hoc comparisons are calculated.

Explanation / Answer

a) H0: All the treatments means are equal

H1: Atleast one treatment mean is not equal.

alpha:5%

b) Test statistic:

From Excel

F cal=6.3012

C) P value=0.01345

d) alpha=5%

e) P <0.05 we reject the null hypothesis

Anova: Single Factor SUMMARY Groups Count Sum Average Variance treatment 1 5 46.34 9.268 0.39667 treatment 2 5 57.01 11.402 0.55577 treatment 3 5 49.72 9.944 1.87903 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 11.89449 2 5.947247 6.301229 0.013465 3.885294 Within Groups 11.32588 12 0.943823 Total 23.22037 14

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