1. Calculate the Variance for each lake  2. Plug values into the t-test equation and find 'calculated t' 3. Determine the df and look up 'critical t' with a p-value of 0.05

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
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1. Calculate the Variance for each lake 

2. Plug values into the t-test equation and find 'calculated t'

3. Determine the df and look up 'critical t' with a p-value of 0.05

The following data were taken from a research article in the Canadian Journal of
Fisheries and Aquatic Sciences, Vol. 57, page 126-127 (2000). The study examined the
concentration of various heavy metals in the soft tissues of 2 species of snails in two
different lakes along the St. Lawrence River.
Cadmium (Cd) levels (microgram/gram dry weight) in soft tissues of Physa
gyrina collected in Lake St. Pierre (LSP) and in Lake St. Louis (LSL) in 1990 and 1991
respectively.
LSL
LSP
7.46
1.02
0.64
1.15
0.40
3.74
0.77
0.71
-----
2.24
-----
0.77
0.96
0.37
0.75
0.45
1.33
1.91
1.00
0.85
Transcribed Image Text:The following data were taken from a research article in the Canadian Journal of Fisheries and Aquatic Sciences, Vol. 57, page 126-127 (2000). The study examined the concentration of various heavy metals in the soft tissues of 2 species of snails in two different lakes along the St. Lawrence River. Cadmium (Cd) levels (microgram/gram dry weight) in soft tissues of Physa gyrina collected in Lake St. Pierre (LSP) and in Lake St. Louis (LSL) in 1990 and 1991 respectively. LSL LSP 7.46 1.02 0.64 1.15 0.40 3.74 0.77 0.71 ----- 2.24 ----- 0.77 0.96 0.37 0.75 0.45 1.33 1.91 1.00 0.85
Expert Solution
Working
LSL LSP (x-xbar)^2 (y-ybar)^2
7.46 1.02 29.87716 0.039006
1.15 0.64 0.712336 0.033306
3.74 0.4 3.048516 0.178506
2.24 0.77 0.060516 0.002756
0.77 0.71 1.498176 0.012656
0.37 0.96 2.637376 0.018906
0.45 0.75 2.383936 0.005256
1.91 1.33 0.007056 0.257556
1   0.988036  
0.85   1.308736  

 

The mean is given by

\overline{x} = \frac{1}{n}\sum x

  • LSL
    \overline{x} =1.994

  • LSP
    \overline{y} =0.8225

The standard deviation is given by
\sigma =\sqrt{\frac{1}{n-1}\sum (x - \overline{x})^2}

  • LSL
    s_{1}=2.1736

  • LSP
    s_{1}=0.2798
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