Question

The carapace lengths (in mm) of crayfish were recorded for samples from two sections of a stream

in Kansas.

section1 5, 11, 16, 8, 12

section2 17, 14,15, 21,19, 13

Use the data in problem above to test for a difference between the two sections using the Mann-Whitney U test.

a. Cite the critical values (from Table A4) for a two-sided test at α = 0.05. Remember that the critical-values given in the table are for one-sided tests. Write a decision rule using these critical values.

b. Use the format as stated for problems in above.

Format of answers: for each problem

1. include your hypotheses

2. decision rule include the critical values from Table A3 if n, m are on the table

3. Give the value of the test statistic and the corresponding exact p-value

4. Give a statistical decision: Reject H0 or Fail to Reject H0

5. If there is a context to the problem then write a conclusion in the context of the problem.

Feel free to leave message if you have any question.

Answer 1

H₀: η₁ - η₂ = 0

H₁: η₁ - η₂ ≠ 0

= 0.05

Critical value = 1.96

Test stat = -2.191

Decision: Reject Ho

P-value = 0.0285

Statement: There is a statistical difference between the two sections.

Section 1	Section 2
5	17
11	14
16	15
8	21
12	19
	13
	n	sum of ranks
	5	18	Section 1
	6	48	Section 2
	11	66	total
		30.000	expected value
		5.477	standard deviation
		-2.191	z
		.0285	p-value (two-tailed)