To investigate the effect of two recent national Danish aquatic environment e co

Question

To investigate the effect of two recent national Danish aquatic environment e concentration of nitrogen (measured in g/m3) has been measured in a enforced in 1998 and particular river just before the national action plans were 2003 respectively, and also in 2011. Each measurement is repeated 6 times over a short stretch of the river. The following output from R correspond to a one-way analysis of variance. However, most of the numbers are replaced by letters. Analysis of Variance Table Response: Nitrogen Df SumSq MeanSq Fvalue PrF Year AB Error D 24.0 Total F 36.8 (o) Write down the actual mumbers jist below the letters. (b) Estimate the population standard deviation of the measurements. (c) What percentage of total variation is explained by the ANOVA model? differences in the mean Nitrogen values from year to year? (i) Define the parameter(s) carefully. (ii) Write down the hypotheses. (ii) State you decision, and (iv) Write down the conclusion in context. (d) Can you demonstrate statistically significant (at significance level a-0.05) Let.

Explanation / Answer

a)

A: k-1 =3-1=2

D: 18-3 =15

F: 18-1 =17

B= 36.8-24=12.8

C = B/A = 6.4

E =24/15 =1.6

U = C/E =6.4/1.6 =4

from the F table V = 0.9594748

b)

SD = 36.8 /sqrt(17) = 8.9

c)

=1- SSE/SST = 1 -24/36.8 =0.3478261

d)

Ho= mean nitrogen levels are same

H1=At least one nitrogen level is different

We calculate the F statsitc

FroM A we see that at .05 P valvue is .9

which is > .05 so we fail to reject null hypothesis

so, the the nitrogen levels are not statistically different.

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