UNIVERSITY OF EAST ANGLIA
School of Biological Sciences
Main Series UG Examination 2012-2013
MODELLING AND STATISTICS FOR BIOLOGISTS
BIO-1A7Y
Time allowed: 2 hours
Answer ALL questions in ALL sections
Write EACH answer in the spaces provided after each question on the EXAM SCRIPT
Where appropriate provide answers in standard form and with a number of significant
figures/decimal places appropriate to the individual question.
The maximum number of marks available for your answers in SECTION A is 25 marks
The maximum number of marks available for your answer in SECTION B is 25 marks
The maximum number of marks available for your answer in SECTION C is 50 marks
The TOTAL number of marks available for the paper is 100
Numbers in square brackets [ ] indicate the relevant mark applied to each part of the
question.
Notes are not permitted in this examination.
Do not turn over until you are told to do so by the Invigilator.
Graph paper will be provided
BIO-1A7Y
Copyright of the University of East Anglia
Module Contact: Dr Harriet Jones, BIO
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SECTION A
Answer ALL questions.
1.
Convert 346 ml to litres
[1 mark]
2.
Convert 0.04 dm3 to ml
[1 mark]
3.
Convert 84500 m2 to km2
[1 mark]
4.
Convert 3.46 x 10-7 mm2 to µm2
[1 mark]
5.
Convert 8.32 x 10-6 km3 to m3
[1 mark]
6.
Convert 3.87 x 1011 µm3 to m3
[1 mark]
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7.
Answer BOTH parts (a) and (b)
(a)
A population of leafcutter ants cleared 48 cm3 of leaves in 50 min. Working at
the same continuous rate, how much leaf volume would they clear in 12 h?
[2 marks]
(b)
The leaves approximate in shape to an ovoid with surface area, A, where
.where r1 = 2.3 cm and r2 = 1.8 cm. The average depth of a leaf is 0.3 mm.
Calculate the number of leaves cleared in 50 min
[2 marks]
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8.
An albatross can fly without landing for five years, flying at approximately 10
-1
m s . Taking the circumference of the Earth to be 40,075 km, and assuming the
Earth to be spherical, how many times could the albatross fly around the Earth in
five years (assume each year to equal exactly 365 days)?
[2 marks]
9.
A bacterial cell can be approximated to a cylinder with a circumference of
0.15 µm and a length of 1.05 µm. Calculate its volume.
[2 marks]
10.
A blackcurrant bush has 4500 blackcurrants on it. The currants each
approximate to a sphere and have a mean diameter of 1.2 mm. Calculate the total
volume of blackcurrants in m3 from this one bush. The volume of a sphere, V, is
given by
, where r is the sphere radius.
[2 marks]
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11.
Calculate the number of moles of boric acid in 4.2 mg boric acid. The molar
mass of boric acid is 61.83 g mol-1.
[1 mark]
12.
Calculate the molarity of a solution where 7.85 mg KCl has been dissolved in
water to give a final volume of 45 ml. The molar mass KCl is 74.55 g mol-1. [2 marks]
13.
How much of a 4.6 mmol l-1 (mM) stock solution of NaOH would be required
to make 50 ml of a solution of 5.5 µmol l-1 NaOH?
[2 marks]
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14.
Students were asked to make up a 200 ml solution which contained NaCl and
KCl with final molarities of 4 mmol l-1(mM) NaCl and 6.2 mmol l-1(mM) KCl. They
were provided with NaCl as a crystalline solid, and KCl as a stock solution where 5 g
KCl had been dissolved in water to a final volume of 500 ml. How much of solid
NaCl, and what volume of the KCl stock solution, will be required to make the final
solution? The molar masses of NaCl and KCl are 58.44 g mol-1 and 74.55 g mol-1,
respectively.
[4 marks]
END OF SECTION A
Section B begins on next page/ . . .
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SECTION B
Answer ALL questions
15.
Answer ALL parts (a), (b) and (c).
Between 1970 and 1990 the population, N, of Mexico City grew exponentially as a
function of time, t, with rate constant, k. The corresponding growth model is given by,
N  N 0e kt
where N0 is the population at t = 0.
(a)
If the population of Mexico City was 9.4 million in 1970 and had grown to 20.2
million by 1990, find the values for the parameters N0 and k of the exponential
growth model.
[4 marks]
(b)
By what year does your parameterized growth model predict that the
population will reach 50 million?
[4 marks]
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(c)
Why is an exponential growth model unlikely to provide accurate estimates of
population over the period suggested by your answer to part (b)? Suggest an
alternative model for growth which might be used to provide better population
estimates.
[3 marks]
16.
Answer ALL parts (a), (b) and (c).
A researcher proposes that the number of individuals, N, in a population grows with
time, t, according to the following differential equation,
dN
 At k
dt
The number of individuals in the population recorded as a function of time in years is
given in the table below (Table 1). You may assume that N = 0 when t = 0.
Table 1. Number in a population over six years
Time(Year)
1
2
3
4
5
6
Population(/103
thousands)
1.5
5.6
12.7
22.3
35.0
50.1
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(a)
Find by integration the general solution to the differential equation. [5 marks]
(b)
Use the stated initial conditions and your answer to part (a) to find the specific
solution to the differential equation.
[3 marks]
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(c)
Use a suitable graphical method to determine approximate values for the
parameters (A and k) of the growth model.
[6 marks]
END OF SECTION B
Section C begins on next page/ . . .
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SECTION C
Answer ALL questions
17.
Answer ALL parts (a), (b), (c) and (d).
Two samples of wheat, grown with different fertilizers (A and B), were collected.
Data showing plant height (cm) for 5 plants in each sample are provided below
(Table 2):
Table 2. Plant height with two different fertilizers
Plant height (cm)
Fertilizer A
Fertilizer B
35
32
36
28
28
36
31
27
40
32
(a)
Calculate means for samples A and B.
[1 mark]
(b)
Given that the standard deviation for sample A = 4.6 cm and for sample
B = 3.6 cm, calculate the standard error.
[1 mark]
(c)
Calculate the 95% confidence intervals for these two samples.
[1 mark]
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(d)
Can we say that the fertilizers are having different effects on the growth of the
plants at the 5% significance level?
[1 mark]
18.
Why is a paired t-test superior to an independent two samples t-test? [1 mark]
19.
Under what circumstances would you use a Bonferroni correction?
20.
Answer ALL parts (a), (b), (c), (d), (e), (f) and (g).
[1 mark]
A new cancer drug has been developed and tests are carried out to determine
whether or not it slows the growth of tumours. Twenty mice with similar sized
tumours are randomly divided into two groups. One group of mice is injected with the
drug and the other group is used as a control. After two weeks the mice were
sacrificed and the tumours were weighed. The data collected are summarised below
(Table 3, Fig 1).
Table 3. PASW output data
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Figure 1. Mean±s.e. tumour weighting under different treatments (Drug vs
Control)
(a)
What do the summary statistics and graph suggest about these data?
[2 marks]
(b)
What is your null hypothesis for analysis of these data?
[1 mark]
(c)
What two things do you need to check before performing a t-test on these
data?
[2 marks]
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(d)
Below (Table 4) is a PASW output from one of those checks.
Table 4. Kolmogorov-Smirnov PASW output summary
Write a sentence describing what this output is telling you about this check.
[1 mark]
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(e)
The following table (Table 5) is the output providing the results of performing
a t-test with these data in PASW.
Table 5. Independent samples t-test output summary from PASW
What does the Levene’s test tell you about these data?
[1 mark]
(f)
[2 marks]
Which row of t-test information should you use, and why?
(g)
Is this drug effective at changing the size of tumours? Write a sentence
summarising the results of this experiment.
[1 mark]
21.
Why is it better to conduct an ANOVA rather than multiple t-tests when there
are more than 2 data samples?
[1 mark]
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22.
When would you use a Kruskal Wallis test as opposed to an ANOVA?
[1 mark]
23.
Name two tests that can be used to test for associations.
[1 mark]
24.
What is the difference between the Pearson and Spearman correlation
coefficients?
[1 mark]
25.
What is a non-parametric statistical test?
[1 mark]
26.
Between what two numbers do correlation coefficients vary?
[1 mark]
27.
What does the value of r2 in a regression analysis indicate?
[1 mark]
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28.
On which axis (x or y) would you plot the independent variable in a regression
analysis?
[1 mark]
29.
What is the definition of the line of best fit?
30.
Answer ALL parts (a), (b), (c), (d), (e) and (f).
[1 mark]
The following (Table 6, Fig 2) are data, and a summary graph, of the mass (in g) of
neonatal female mice whose mothers were maintained on 4 different diets:
Table 6. Mass of mice (g) on different diets.
Mass (g)
Individual
Diet 1
Diet 2
Diet 3
Diet 4
1
2
3
4
5
6
4.6
5.0
4.7
4.3
4.6
4.9
4.8
4.5
5.0
4.6
4.5
5.2
3.8
3.9
4.2
4.0
3.5
3.6
3.9
3.9
4.1
3.5
3.6
4.1
Mean
se
4.68
4.76
3.83
3.85
0.101
0.117
0.105
0.102
Figure 2: Mass in g (mean ± standard error, s.e.) of neonatal female mice born
to mothers maintained on 4 different diets
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(a)
What do the summary statistics and summary graph suggest about these
data?
[3 marks]
(b)
What 3 checks should you make before subjecting these data to ANOVA?
[3 marks]
(c)
The following (Table 7) is the ANOVA output from these data.
Table 7. Output summary data from PASW for an ANOVA
ANOVA
Weights
Sum of Squares df Mean Square
Between Groups
4.703
3
Within Groups
1.370 20
Total
6.073 23
F
Sig.
1.568 22.887 .000
.068
Describe what the results of this test mean.
[1 mark]
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(d)
Following the ANOVA, the following Tukey tests for multiple comparisons
were done (Tables 8 and 9).
Table 8. Output from PASW
Multiple Comparisons
Weights
Tukey HSD
(I) Diet (J) Diet
95% Confidence Interval
Mean Difference (I-J) Std. Error
1.00
2.00
4.00
Lower Bound Upper Bound
2.00
-.08333
.15111
.945
-.5063
.3396
3.00
*
.15111
.000
.4271
1.2729
4.00
*
.83333
.15111
.000
.4104
1.2563
1.00
.08333
.15111
.945
-.3396
.5063
3.00
*
.15111
.000
.5104
1.3563
*
.15111
.000
.4937
1.3396
*
.15111
.000
-1.2729
-.4271
*
.85000
.93333
4.00
3.00
Sig.
.91667
1.00
-.85000
2.00
-.93333
.15111
.000
-1.3563
-.5104
4.00
-.01667
.15111 1.000
-.4396
.4063
1.00
*
.15111
.000
-1.2563
-.4104
*
.15111
.000
-1.3396
-.4937
.15111 1.000
-.4063
.4396
-.83333
2.00
-.91667
3.00
.01667
*. The mean difference is significant at the 0.05 level.
Table 9. Output data from PASW
Homogeneous Subsets
Weights
Tukey HSD
Diet
a
Subset for alpha = 0.05
N
1
2
3.00
6
3.8333
4.00
6
3.8500
1.00
6
4.6833
2.00
6
4.7667
Sig.
1.000
.945
Means for groups in homogeneous subsets are displayed.
a. Uses Harmonic Mean Sample Size = 6.000.
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Describe what these tests (Table 8 and Table 9) show.
[2 marks]
(e)
We are now told that diets 1 and 2 contain normal amounts of protein, but are
low in sucrose or glucose, respectively. Diets 3 and 4 contain normal amounts of
sugar but are low in either protein or Vitamin D, respectively. Using this information,
write a results section for the whole of the analyses done, above, and describe what
it all mean in terms of the biology.
[2 marks]
(f)
What further tests or information would you need in order to confirm or test
your ideas from (e)?
[2 marks]
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31.
Answer ALL parts (a), (b), (c) and (d).
An experiment was conducted to test whether the polychaete worm Nereis
diversicolor can withstand zinc pollution by actively regulating zinc levels within their
bodies. The following data (Table 10) were obtained on the internal zinc [Zn2+]
concentration in worms grown in water containing various concentrations of zinc.
Table 10. Zinc [Zn2+] concentration in worms and water (μg g-1)
[Zn2+]
Water
1.96
2.27
2.46
2.65
2.86
2.92
3.01
3.24
3.37
3.49
Worms
2.18
2.23
2.22
2.27
2.25
2.30
2.31
2.34
2.36
2.35
(a)
If you were to plot these data on a scattergraph, which would you designate
as the dependent variable and on which axis would you plot it?
[2 marks]
(b)
These data were subjected to a regression analysis to test the effect on
external zinc concentration on internal zinc concentration in the worm. The following
(Table 11) is the ANOVA output of a PASW regression analysis.
Table 11. PASW output data
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Describe this statistical result. What does it indicate about whether external zinc
concentration affects the internal zinc levels in the worm?
[3 marks]
(c)
The following (Table 12) output contains the coefficients of the line of best fit:
Table 12. PASW output summary
From this output extract and write down the equation of the line of best fit. [2 marks]
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(d) Write up the statistical tests and your conclusions fully as if for a practical write
up, including what further tests you would do to confirm your ideas.
[5 marks]
END OF PAPER
BIO-1A7Y
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BIO-1A7Y EXAMINATION MARKERS 2012-13
Question No.
Section A
Section B
Section C
BIO-1A7Y
1st Marker
Dr H Jones
Dr A Hemmings
Prof T Chapman
2nd Marker
n/a
n/a
n/a
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