Three products were used in a hot summer to keep the pool chlorine level high. Each product was used in 6 pools, and there was a total of 18 pools in the experiment. The same amount of chlorine was added to each pool (A, B, or C) and the conditions such as pool size, temperature, sun exposure etc. were similar. The chlorine levels (%) were measured and recorded after 24 hours of using the products. The percentages in the table below are the percentage of the chlorine added to the pool remaining after this 24 hours. The data is as follows: A 96 56 52 66 70 60 B 44 36 34 50 40 48 с 34 40 32 22 20 24 a) Find the overall mean of the chlorine level across all the pools measured, and then find the mean of the chlorine level for each product.

Three products were used in a hot summer to keep the pool chlorine level high. Each product was used in 6 pools, and there was a total of 18 pools in the experiment. The same amount of chlorine was added to each pool (A, B, or C) and the conditions such as pool size, temperature, sun exposure etc. were similar. The chlorine levels (%) were measured and recorded after 24 hours of using the products. The percentages in the table below are the percentage of the chlorine added to the pool remaining after this 24 hours. The data is as follows: A 96 56 52 66 70 60 B 44 36 34 50 40 48 с 34 40 32 22 20 24 a) Find the overall mean of the chlorine level across all the pools measured, and then find the mean of the chlorine level for each product.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Three products were used in a hot summer to keep the pool chlorine level high. Each product was
used in 6 pools, and there was a total of 18 pools in the experiment. The same amount of chlorine
was added to each pool (A, B, or C) and the conditions such as pool size, temperature, sun exposure
etc. were similar. The chlorine levels (%) were measured and recorded after 24 hours of using the
products. The percentages in the table below are the percentage of the chlorine added to the pool
remaining after this 24 hours. The data is as follows:
A
96
56
52
66
70
60
B
44
36
34
50
40
48
с
723227
34
40
20
24
a) Find the overall mean of the chlorine level across all the pools measured, and then find the
mean of the chlorine level for each product.

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Step 1: Given Information

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Step 2: Calculation of mean of chlorine level for product A.

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Step 3: Calculation of mean of chlorine level for product B.

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Step 4: Calculation of mean of chlorine level for product C.

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Step 5: Calculation of overall mean for chlorine level across all pools measured

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Follow-up Questions

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Follow-up Question

e)Write the conclusion based on the ANOVA table.

Solution

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Follow-up Question

d) Perform an ANOVA test using the statistical package of your choice.
Copy and paste the resultant ANOVA table into your assessment document and compare your
calculated residual mean square from part c)
with the residual mean square from this ANOVA table.

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Follow-up Question

c) Calculate the residual sum of squares, then find the mean of the residual sum of
squares.
Note: residual mean square= (residual sum of squares) / (residual degrees of freedom)
where, residual degrees of freedom =
(A sample size -1) + (B sample size -1) + (C sample size -1)
Hint: you can use Microsoft Excel, R or SPSS to perform this calculation)

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Follow-up Question

b) If each observation is given by the overall mean + product effect + residual, find the
residuals for all above observations and write them in a table. Product effect for
each observation is:
the group mean - the overall mean
So, the product effect is the same for all observations in a group (e.g., A).
(Hint: you can use Microsoft Excel, R or SPSS for this)

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