The following data indicate numbers
and weights of largemouth bass caught at Lakes Acorn and Bacon. Each of
ten samples from each lake were based on 10 man-hours of fishing effort.
Weights of fish weighing less than one pound ("small fish") are not included.
LAKE ACORN
number of
sample
small fish
weights of fish over one pound (+0.1 lb)
1 13 1.6, 3.1, 5.1, 5.3
2 5 1.2, 2.1, 2.4
3 2 3.6
4 4 2.5, 2.5, 3.1, 3.4
5 8 1.6, 2.0, 3.1
6 15 1.1, 2.0, 2.4
7 7 1.4
8 10 2.0, 2.4, 2.4, 2.5
9 4 3.0, 3.4
10
7
1.4, 2.0, 2.9, 4.6
LAKE BACON
number of
sample
small fish
weights of fish over one pound (+0.1 lb)
1 8 1.2, 1.2, 1.4, 1.5, 2.6, 2.6
2 9 1.2, 1.4, 1.4, 1.5, 1.5, 2.6, 3.1
3 14 1.1, 1.2, 1.2, 1.4, 2.1
4 21 1.4, 1.5
5 16 1.5, 1.5, 1.5, 1.5, 1.5, 1.5, 2.2
6 13 1.1, 1.3, 1.6, 1.6, 1.6, 1.6, 1.9
7 10 1.1, 1.1, 1.2, 1.6, 1.8, 2.1
8 8 1.2, 1.2, 1.3
9 6 1.1
10
7
1.3, 1.3, 1.4, 2.8
Carry out a Rank Sum Test to determine if there was a significant difference between Lake Acorn and Lake Bacon in the number of fish caught weighing > 1.5 pounds. In order to receive full credit, your answer (on a separate sheet of paper) must contain:
1. The two sets of data, appropriately ranked
2. Correct calculations for "T" and "Tcrit"
3. Whether or not you can reject the null hypothesis
4. A complete sentence (or two) that
describes the outcome of the statistical test
HERE IS THE SOLUTION FOR THE PROBLEM
ABOVE:
(Note that the data consist of two samples of 10 for each lake.)
Lake Acorn Lake Bacon
# of fish rank # of fish rank
4 16.5 3 12.5
2 9 4 16.5
1 5.5 1 5.5
4 16.5 1 5.5
3 12.5 7 20
2 9 5 19
0 2 3 12.5
4 16.5 0 2
2 9 0 2
3 12.5 1 5.5
SUM = 109
SUM = 101
T = smaller sum = 101
Tcrit = 78
You cannot reject the null hypothesis.
There was no significant difference between Lake Acorn and Lake Bacon regarding the numbers of bass taken weighing at least 1.5 pounds (Rank Sum Test, p>0.05).