Problem Set F A species of non-native fish was accidentally introduced into a la

Question

Problem Set F A species of non-native fish was accidentally introduced into a lake where an endangered native fish species is found. Although the introduced species does not attack or eat the native species, it does have the same dietary preference as the native fish. Scientists, afraid that the introduced species may be indirectly out-competing the native species for food, decided to do a short-term experiment. They collected 10 samples of the native fish species, weighed each one, and tagged each fish with its own unique ID number (1-10). After 3 months, the scientists started trapping all the fish in the lake until they located the exact same fishes that they weighed three months earlier. They took the new weight of the fishes and compared these with their weights three months before. Fish # Original Weight (kg) 10.3 11.4 10.9 12.0 10.0 11.9 12.2 12.3 11.7 12.0 + 3 months Weight (kg) 12.2 12.1 13.1 11.9 12.0 12.9 11.4 12.1 13.5 12.3 9 10 The scientists decided to use a non-parametric test to analyze their data, since no one knew any parametric tests at that time. parametric test compatible with their data, and decided to use it instead After they finished computing, one of them suddenly remembered

Explanation / Answer

H0: The median difference is zero versus

H1: The median difference is positive

=0.05

W-value: 8
Mean Difference: -0.63
Sum of pos. ranks: 8
Sum of neg. ranks: 47

Z-value: -1.9876
Mean (W): 27.5
Standard Deviation (W): 9.81

Sample Size (N): 10

The Z-value is -1.9876. The p-value is 0.0466. The result is significant at p 0.05.

The W-value is 8. The critical value of W for N = 10 at p 0.05 is 8. Therefore, the result is significant at p 0.05.

origina weight (kg) +3 month weight (kg) SIGN ABSOLUTE DIFFERENCE RANK SIGN RANK 10.3 12.2 -1 1.9 8 -8 11.4 12.1 -1 0.7 4 -4 10.9 13.1 -1 2.2 10 -10 12 11.9 1 0.1 1 1 10 12 -1 2 9 -9 11.9 12.9 -1 1 6 -6 12.2 11.4 1 0.8 5 5 12.3 12.1 1 0.2 2 2 11.7 13.5 -1 1.8 7 -7 12 12.3 1 0.3 3 -3

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