Question

4. A field recently fertilized with manure is believed to have caused excessive levels of nitrate in an adjacent pond. Twenty-five samples were collected and analyzed using a field test kit. Conduct both the Dixon Ratio, and the Grubb's test to determine if there are any outliers present in the accompanying data set?

pls help!!

Answer 1

Firstly arrange the data in ascending form as follows :

21
22
22
24
24
25
26
26
26
28
28
29
29
31
32
33
34
34
34
37
37
38
38
38
83

The sample mean is 31.96 and standard deviation is 11.95 (pls note degree of freedom is 24)

For Dixon ration calculate the ratio R22 = X_n - X _n-2 / X_n - X₃ = 83-38 / 83-22 = 0.73

The critical value for this ratio is 0.46 at 5% level of significance. As 0.73 > 0.46 the null hypothesis is rejected that there is no outlier. 83 is thus the outlier.

For the Grubb test calculate G = Max I X - Sample Mean I / Standard deviation

The maximum value that is got is 4.27113 when X is 83. The critical value for this is 2.82 when n=25.

As 4.27 > 2.82, the null hypothesis is rejected.

NB

The data needs to be checked for normality first before these tests can be done. I have assumed normality.