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Hypothesis Testing: Considering the Wilcoxon Test

It has been suggested that daily production of a subassembly would be increased if better portable lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. The number of subassemblies produced per week by a sample of employees is attached. Using the Wilcoxon signed-rank test, determine whether the suggested changes are worthwile.
a. state the null hypothesis
b. decide on the alternative hypothesis
c. decide on the level of significance
d. state the decision rule
e. compute t and arrive at a decision

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please refer to the attachment.

Employee Past Production Production After Employee Past Prod Prod after Installing Lighting etc
Record Installing Lighting etc Record

JD 23 33 WWJ 21 25
SB 26 26 OP 25 22
MD 24 30 CD 21 23
RCF 17 25 PA 16 17
MF 20 19 RRT 20 15
UHH 24 22 AT 17 9
IB 30 29 QQ 23 30

WILCOXON SIGNED RANK TEST : nonparametric equivalent to paired t-test
ASSUMPTIONS:
- Each paired difference comes from a quantitative distribution that is symmetric, with the same center of symmetry (= median); use Sign test is not ...

Solution Summary

It has been suggested that daily production of a subassembly would be increased if better portable lighting were installed and background music and free coffee and doughnuts were provided during the day. Management agreed to try the scheme for a limited time. The number of subassemblies produced per week by a sample of employees is attached. Using the Wilcoxon signed-rank test, determine whether the suggested changes are worthwile.
a. state the null hypothesis
b. decide on the alternative hypothesis
c. decide on the level of significance
d. state the decision rule
e. compute t and arrive at a decision

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