Question

You may need to use the appropriate appendix table or technology to answer this question.

The following data are product weights for the same items produced on two different production lines.

Line 1	Line 2
13.6	13.7
13.8	14.1
14.0	14.2
13.9	14.0
13.4	14.6
13.2	13.5
13.3	14.4
13.6	14.8
12.9	14.5
14.4	14.3
	15.0
	14.9

Test for a difference between the product weights for the two lines. Use α = 0.05.

State the null and alternative hypotheses.

H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0 H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.     H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical. H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0 H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

    Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Answer 1

Trt A	Trt B	rank for sample 1	rank for sample 2
13.6	13.7	6.5	8
13.8	14.1	9	13
14	14.2	11.5	14
13.9	14	10	11.5
13.4	14.6	4	19
13.2	13.5	2	5
13.3	14.4	3	16.5
13.6	14.8	6.5	20
12.9	14.5	1	18
14.4	14.3	16.5	15
	15		22
	14.9		21

Trt A          
sample size ,    n1 =    10  
sum of ranks ,    R1 =    70  
          
Trt B          
sample size ,    n2 =    12  
sum of ranks ,   R2 =    183  
          
W=sum of ranks for smaller sample size =       70  
================

H0: The two populations of product weights are identical.
Ha: The two populations of product weights are not identical.

test stat, W = 70

p value = 0.0030

(please try 0.0020, if above gets wrong)

Reject H0. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.