Question

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

Line 1	Line 2
13.6	13.4
13.9	14.2
14.0	14.5
13.8	14.0
13.1	14.6
13.5	13.7
13.3	14.1
13.6	14.9
12.8	14.7
14.1	14.3
	15.0
	14.8

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: 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 not identical.
H_a: The two populations of product weights are identical.

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

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.

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.  

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.

Answer 1

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

sample size n1		group 1	10
sample size n2		group 2	12
Rank sum (R1)=		group 1	68
Rank sum (R2)=		group 2	185
test statistic W=R1=			68

sample mean =

μ=n1(n1+n2+1)/2=

115

Variance=	σ2=n1n2(n1+n2+1)/12=		230.00
standard deviation= σ =			15.17

test stat z=

Z=(U-μ)/σ

=

-3.07

p value    =

0.0022 (please try 0.0021 if this comes wrong)

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