Name:
STAT 305 - Final Examination
Date: May 6, 2025
1. (10 pts) The log(concentration ratio) of polymers was being investigated for two groups of materials.
Perform a Wilcoxon rank sum test and fill in the blank table cells in the table below, and then show
worked equations. Assume α = 0.05.
ID xi R(xi ) Group R(x ∈ grp1) R(x ∈ grp2)
1 -0.177 1
2 -0.234 1
3 0.067 1
4 -0.246 1
5 -0.096 2
6 -0.057 2
7 0.225 2
8 0.351 2
R1 = R2 =
a). (2 pts) What is the conclusion of the test?
b). (2 pts) What is the decision rule (reject/accept null hypothesis)?
c). (2 pts) Is p < 0.05 or p ̸< 0.05?
, 2. (10 pts) The difference in resistance (ohms) was being studied for two manufactured electrical com-
ponents: a “New” component and the currently manufactured “Old” component. Perform a Wilcoxon
signed rank test for matched pairs data and fill in the blank table cells in the table below, and then
show worked equations. Assume α = 0.05.
ID Old New di |di | R(|di |) R(|di | | d− ) R(|di | | d+ )
1 -0.177 -0.034
2 0.067 -0.046
3 -0.096 0.143
4 0.225 0.551
5 -0.154 0.387
6 -0.180 0.109
7 -0.341 0.577
8 0.360 0.242
R(d− ) = R(d+ ) =
P P
a). (2 pts) What is the conclusion of the test?
b). (2 pts) What is the decision rule (reject/accept null hypothesis)?
c). (2 pts) Is p < 0.05 or p ̸< 0.05?
STAT 305 - Final Examination
Date: May 6, 2025
1. (10 pts) The log(concentration ratio) of polymers was being investigated for two groups of materials.
Perform a Wilcoxon rank sum test and fill in the blank table cells in the table below, and then show
worked equations. Assume α = 0.05.
ID xi R(xi ) Group R(x ∈ grp1) R(x ∈ grp2)
1 -0.177 1
2 -0.234 1
3 0.067 1
4 -0.246 1
5 -0.096 2
6 -0.057 2
7 0.225 2
8 0.351 2
R1 = R2 =
a). (2 pts) What is the conclusion of the test?
b). (2 pts) What is the decision rule (reject/accept null hypothesis)?
c). (2 pts) Is p < 0.05 or p ̸< 0.05?
, 2. (10 pts) The difference in resistance (ohms) was being studied for two manufactured electrical com-
ponents: a “New” component and the currently manufactured “Old” component. Perform a Wilcoxon
signed rank test for matched pairs data and fill in the blank table cells in the table below, and then
show worked equations. Assume α = 0.05.
ID Old New di |di | R(|di |) R(|di | | d− ) R(|di | | d+ )
1 -0.177 -0.034
2 0.067 -0.046
3 -0.096 0.143
4 0.225 0.551
5 -0.154 0.387
6 -0.180 0.109
7 -0.341 0.577
8 0.360 0.242
R(d− ) = R(d+ ) =
P P
a). (2 pts) What is the conclusion of the test?
b). (2 pts) What is the decision rule (reject/accept null hypothesis)?
c). (2 pts) Is p < 0.05 or p ̸< 0.05?
