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Your company is deciding which of four machines to purchase for a production line

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Your company is deciding which of four machines to purchase for a production
line. The machines are all designed to fill and close bottles of liquid detergent. Each
machine is tested for the same period of time on 10 separate occasions in a completely randomized design.

See attached file for full problem description.

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1. Your company is deciding which of four machines to purchase for a production
line. The machines are all designed to fill and close bottles of liquid detergent. Each
machine is tested for the same period of time on 10 separate occasions in a
completely randomized design.
The results are:
Bottles filled per minute by machine
Time period A B C D
1 251.2 263.2 269.7 251.6
2 245.1 262.9 263.2 248.6
3 248.0 265.0 277.5 249.4
4 251.1 254.5 267.4 242.0
5 260.5 264.3 270.5 246.5
6 250.0 257.0 265.5 251.3
7 253.9 262.8 270.7 261.8
8 244.6 264.4 272.9 249.0
9 254.6 260.6 275.6 247.1
10 248.8 255.9 266.5 245.9

Conduct an F-test to test the hypothesis that the population means for machines A,
B, C and D are equal. State the assumptions that are necessary to ensure the validity
of the test. Interpret the result.

2. company you work for employs 585 assembly-line workers - 526 men and 59
women. 16 men and 10 women have been selected to be laid off.
You have been consulted as a statistical expert, because your company is concerned
that the 10 women who are to be laid off may sue the company, claiming that they
have been discriminated against.

You have been asked to:
a) Construct the strongest possible argument that the laid off women could make in favor
of their assertion that they have been discriminated against.
b) Identify the assumptions that underlie the argument made in a)
c) Defend the layoffs by showing that the assumptions in b) are inconsistent with a claim
- if it can be proved - that the company chose the 26 workers to lay off based solely on
performance-based criteria.