Homework #7 BES 301   Autumn 2005

 

 

Reading Assignment (revised):

  • For Nov 28 and 30, read Valiela Chs 8-9,  and Hatton, pp 59-80. :  (skip ch 10 of Valiela)
  • For Mon, Dec 5, read Hatton 81-86 and 93-105
  • For Wed, Dec 7, read paper by Gould and paper by Meyer (213-18 and 230-34).  Both papers are on e-reserve.. 

Take notes in your class journal.  Be prepared to participate or take the lead in a class discussion on aspects of these readings.

 

 

Research Assignment:

Your final literature review report (including synthesis paper) (Assignment #4 of the research project) is due before class on Dec 7, Wednesday.  Details of the assignment can be found in the assignment handout.  Note that late submissions will not be accepted on this final report: no exceptions(see syllabus)!


Individual Written Assignment for Mon, Dec 5.  (to be worked alone, but with consultation on software, methodology, etc.  Also, feel free to contact me by e-mail with any question that may arise.)

Prepare these problems and turn in to E-submit site under assignment “statistics homework” no later than before class on Dec 5.  Work on these alone, but feel free to get help in using the tools.  Feel welcome to go to the quantitative skills center for assistance.  But, do not treat these as group assignments.  Every student needs to be able to do these on their own.  Answer the following, preparing a word document for submission to the e-submit site.  When you use Excel, do not submit the actual spread sheet.  Rather, cut and paste an image of the interesting part of the spreadsheet display into your word document.  Show work for credit.  In the case of the problems to done by hand or with calculator, show sufficient intermediate results for me to be sure you understand it and can do it by hand.  In the case of the problems to be done with Excel, show a snapshot of the spreadsheet to show me that you know how to enter the data and get the calculation accomplished.

 

  1. The following replicated measurements were performed in a laboratory analysis involving titration with a chemical reagent (in mL):  10.08, 10.11, 10.09, 10.10, and 10.12.   Calculate the median, mean (average), standard deviation, and CV (coefficient of variance) for this set of measurements.  Do this with your calculator and show work.

  2. Mean = m=0.500 mg/mL

    Std Dev = s = 0.0165 mg/mL
     
    In measuring nitrate concentration in a water sample, the following results and frequencies were obtained:

    :
    Does this distribution appear to be “normal”?  Explain how you can tell and what you did to make this determination.  If you have work to show, such as a figure, include  it in your document.






  1. Consider the following two analytical procedures for tin in foodstuffs.  The results are reported in mg of tin per kg of food.  These are two different analytical procedures and meet all of the requirements for normal distributions, independence, equal variances, etc.


Procedure

Tin found in foodstuff (mg/kg)

Mean = m

Std Dev = s

A

55

57

59

56

56

59

57.00

1.67

B

57

55

58

59

59

59

57.83

1.60

 

 

 

 

 


           By calculating (using calculator and equations from notes) determine t, and then with the tables given out with the notes determine the p-value.  What does this mean?  Are the two means significantly different?  What is the percentage error for your conclusion?  What is the null hypothesis here?  Is it retained or rejected by this comparison?

  1. Consider the following data, which are four sets of measurements under different conditions of the fluorescence of an environmental chemistry sample:


Conditions

Replicate Measurements

A

102

100

101

B

101

101

104

C

97

95

99

D

90

92

94



Using Excel, perform an ANOVA analysis on this data set, and determine whether or not the four means from these conditions are the same or significantly different.  What is your null hypothesis?  What is the percent chance that a rejection of this null hypothesis would be in error?   Cut and paste a copy of your spreadsheet display to show your work

 

  1. The following absorbance data was obtained in a test for glucose.  The solutions were made up with good accuracy and precision to the specified concentrations (in mM) and then the absorbance was measured with an instrument.  This is measure of how much glucose is present.


Concentration (mM)

0

2

4

6

8

10

Absorbance (unitless)

0.002

0.150

0.294

0.434

0.570

0.704



            Using Excel (or something similar), generate an (x,y) scatter plot of the data.  Include a trend line (linear regression) on the graph and give the equation that is the best fit, and the R2 value for this fit.  Use cut and paste copy techniques to place the resulting figure with equation in the document for this assignment.

 

  1. Consider the paper by Shortle et al that we have already read.
    1.  In the Results and Discussion section find one  instance where they rejected their null hypothesis based on statistics and one where they supported it.  In each case state in your own words what the null hypothesis was and what the statistical justification for rejecting or supporting it was.  Be sure that I know what they concluded in each case.
    2. In the Figure 2 of the Results and Discussion section, several conclusions are formed about relationships based upon regression statistics.  Find a case where the null hypothesis was supported and one where it was rejected.  Explain from the values given how this rejection of H0 was determined.  Simply look at the numbers in the caption and figures and explain in two cases what they mean.  The parameter “adj r2” in the figures is the adjusted R2 mentioned in class this morning; it is almost the same as the ordinary R2 and should be interpreted that way here.