YOUR ASSIGNMENT WAS TO SOLVE TWO STATISTICS PROBLEMS LIKE THE ONE DISPLAYED BELOW:

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                               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).