Question

a kind of fish mullets liza vaigiensis sp have been found in the day and night fishing activities during high tide. The lengths ( in cm ) of the fish were recorded and give as below. Determine whether there is a significant difference in the fish length depending on the catch time.

Night	18	18	20	20	20	21	21	22	23	25
Day	16	17	17	18	18	19	19	19

a) write the null hypothesis

b) write the alternative hypothesis

c) By completing the table below, write the value of P and Q

fish length at Night	18	18	20	20	20	21	21	22	23	25	SUM
Rank	...	...							...	...	P
fish length at Day	16	17	17	18	18	19	19	19	SUM
Rank	1	...					...	...	Q

d) by referring to the table of wilcoxon rank sum test , find the critical value at a=0.05

e) what is the decision of this problem?

f) what is the conclusion?

Answer 1

Let , be the median length of the fishes caught at Night and   be the median length of the fishes caught at Day time. We want to test whether   or not. Suppose, .Then it is enough to test whether or not.

a) write the null hypothesis

ans :- The null hypothesis is -   

b) write the alternative hypothesis.

ans :- The alternative hypothesis is -   

c) By completing the table below, write the value of P and Q.

The combined values and ranks are :

16	17	17	18	18	18	18	19	19	19	20	20	20	21	21	22	23	25
1	2.5	2.5	5.5	5.5	5.5	5.5	9	9	9	12	12	12	14.5	14.5	16	17	18

So, the final table is :

Night	18	18	20	20	20	21	21	22	23	25	SUM
Rank	5.5	5.5	12	12	12	14.5	14.5	16	17	18	127 = P
Day	16	17	17	18	18	19	19	19	SUM	-	-
Rank	1	2.5	2.5	5.5	5.5	9	9	9	44 = Q

d) by referring to the table of wilcoxon rank sum test , find the critical value at a=0.05.

ans:- The critical value is :   and where,

  .

Here, and . So, .

Also , . Thus, and

So,   = and

=

These are the required critical values.

e) what is the decision of this problem?

ans:- Since, P = 127 =our test statistic is > 53 and <137 , so we reject the null hypothesis at .

f) what is the conclusion?

ans :- We conclude that, there is a significance different between the length of the fishesh caught at different times.