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Homework 4

This document provides instructions for Homework 4 which is due on February 14, 2020. It includes two problems to analyze and draw conclusions about experiments. Problem 1 involves comparing three washing solutions using a randomized block design with observations over four days. Problem 2 studies the effect of five ingredients on a chemical reaction time using a Latin square design with five runs per day over five days. Students are asked to analyze the data provided for each problem using a 0.05 significance level.

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165 views2 pages

Homework 4

This document provides instructions for Homework 4 which is due on February 14, 2020. It includes two problems to analyze and draw conclusions about experiments. Problem 1 involves comparing three washing solutions using a randomized block design with observations over four days. Problem 2 studies the effect of five ingredients on a chemical reaction time using a Latin square design with five runs per day over five days. Students are asked to analyze the data provided for each problem using a 0.05 significance level.

Uploaded by

Sandro Morero
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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IMSE511, Homework 4

(Due on February 14, 2020, Submit the PDF file through Canvas)

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Problem 1: Three different washing solutions are being compared to study their effectiveness in
retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and
only three trials can be run on any day. Because days could represent a potential source of
variability, the experimenter decides to use a randomized block design. Observations are taken for
four days, and the data are shown here. Analyze the data from this experiment (use 𝛼 = 0.05) and
draw conclusions. (50 points)

Solution Days
1 2 3 4
1 13 22 18 39
2 16 24 17 44
3 5 4 1 22

1
Problem 2: The effect of give different ingredients (A, B, C, D, E) on the reaction time of a
chemical process is being studied. Each batch of new material is only large enough to permit five
runs to be made. Furthermore, each run requires approximately 1.5 hours, so only five runs can be
made in one day. The experimenter decides to run the experiment as a Latin square so that day and
batch effects may be systematically controlled. She obtains the data as follows.

Analyze the data from this experiment (use 𝛼 = 0.05) and draw conclusions. (50 points)

Solution Day
1 2 3 4 5
1 A=8 B=7 D=1 C=7 E=3
2 C = 11 E=2 A=7 D=3 B=8
3 B=4 A=9 C = 10 E=1 D=5
4 D=6 C=8 E=6 B=6 A = 10
5 E=4 D=2 B=3 A=8 C=8

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