A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article “Effects of Short-Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows” (Australian J. of Dairy Tech., 2004: 199–203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement and a control sample given no supplement, both initially and after a 9-day period.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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A deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article “Effects of Short-Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows” (Australian J. of Dairy Tech., 2004: 199–203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement and a control sample given no supplement, both initially and after a 9-day period.

 

Obs

Init Se

Init Cont

Final Se

Final Cont

1

11.4

9.1

138.3

9.3

2

9.6

8.7

104

8.8

3

10.1

9.7

96.4

8.8

4

8.5

10.8

89

10.1

5

10.3

10.9

88

9.6

6

10.6

10.6

103.8

8.6

7

11.8

10.1

147.3

10.4

8

9.8

12.3

97.1

12.4

9

10.9

8.8

172.6

9.3

10

10.3

10.4

146.3

9.5

11

10.2

10.9

99

8.4

12

11.4

10.4

122.3

8.7

13

9.2

11.6

103

12.5

14

10.6

10.9

117.8

9.1

15

10.8

 

121.5

 

16

8.2

 

93

 

 

 

  • Do the initial Se concentrations for the supplement and control samples appear to be similar? Use various techniques from Descriptive Statistics Lectures including visualizations where appropriate to summarize the data and answer the question posed.

 

Summarize the data using appropriate methods from lectures and then describe how the Final Se concentration values in the treatment group differ from those in the control group.

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