# 1594-Statistical Methods in Environmental Health_VUsolutions.com by vufellows

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```									                 ALLAMA IQBAL OPEN UNIVERSITY
(Department of Home and Health Sciences)

WARNING
1.     PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM
AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2.     SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.

Course: Statistical Methods in Environmental Health (1594)
Level: M. Sc. Environmental Design                 Semester: Autumn, 2011
Total Marks: 100                                           Pass Marks: 40
ASSIGNMENT No. 1
(Units: 1–5)

Q. 1 (a)     In the population of 30,000 persons, 300 have particular disease. If a person
is chosen at random, what is the probability that he does not have the
disease?                                                                 (10)

(b)   The number of days off work as a result of an accident for employees in a
particular industry is shown below.
Times off in days            Number of Employees
1                            279
2                            686
3                            226
4                            172
5                            135
6                            107
7                            104
8–14                           380
15–21                           107
22–29                            48
30–59                            49
60+                             9
If an accident report is chosen at random from the files, what is the
probability that the employee was off work for:
(i)   Less than 3 days      (ii) More than 7 days     (iii) 30 days or more (10)

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Q. 2 (a)   Draw a diagram to illustrate the membership distribution of the Institution of
Environmental Health Officers in 1988.                                    (10)
Retired fellow               240
Retired members              497
Fellows                      158
Members                      5555
Associate members            39
Student members              718
(b)   In the tables below, the table on the left shows the concentration in per
million (ppm) of organo-chorine pesticides (DDE) in human fats found at
post-mortem examinations. Draw a suitable diagram to show the distribution
of values. Describe the shape of the distribution.
Concentration         Number                    Log of            Number
(ppm)                 observed                  Concentration     Observed
0.00-0.49                  7                    0.200-0.399           1
0.50-0.99                30                     0.400-0.599           5
1.00-1.49                27                     0.600-0.799           8
1.50-1.99                16                     0.800-0.999          22
2.00-2.49                  2                    1.000-1.199          32
2.50-2.99                  6                    1.200-1.399          13
3.00-3.49                  6                    1.400-1.599          15
3.50-3.99                  2                    1.600-1.799           3
4.00-4.49                 --                    1.800-1.999           1
4.50-4.99                  2
5.00-5.49                  1                    Total               100
.
.
8.00-8.49                  1
Total                  100

The logarithms of the data were then taken and the frequency distribution of
the log (concentration) is shown on the right. Draw a suitable diagram. How
does this distribution differ from that of the original concentrations? (10)

Q. 3 (a)   A random sample of 6 cows of breed A had daily milk yield in lbs. as 16, 15,
18, 17, 19 and 17. Another random sample of 8 cows of breed B had daily
yields in lbs, as 18, 22, 21, 23, 19, 20, 24 and 21. Test if breed B is better
than Breed A at   0.0005 .                                             (10)
(b)   A wheat researcher is studying the yield of a certain variety of wheat in the
state of Colorado. He has at his disposal five farms scattered throughout the
state on which he can plant the wheat and observe the yield. Describe the

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sampled population and the target population. Under what conditions will
this be a random sample?                                            (10)

Q. 4 (a)   When examined using a particular screening test, diseased persons give
results which are normally distributed with mean 3.3 and standard deviation
0.4. If results on the test greater than 2.3 considered to indicate the need for
further investigation what is the probability that the disease will be missed
using this test?
Persons not suffering from the disease give results which are normally
distributed with mean 2.0 and standard deviation 0.4. What proportion of
normal subjects will unnecessarily undergo the further investigations? (10)
(b)   Systolic blood pressure in a certain population is distributed with mean 115 mm
Hg and standard deviation 14 mm Hg. A group of 225 diabetics was found to
have a mean systolic blood pressure of 120 mm Hg. Is there evidence to suggest
that diabetics have an elevated systolic blood pressure?                    (10)

Q. 5 (a)   In a trail of zinc sulphate on wound healing, 10 patients were given oral zinc
therapy in addition to normal treatment. A further 10 patients received only normal
treatment. The time taken for ‘complete healing” (in day) was a shown.         (10)

Treated with zinc sulphate                   Not treated with zinc sulphate
33                                           40
34                                           46
43                                           48
44                                           53
46                                           63
46                                           71
48                                           85
51                                           93
52                                           121
61                                           181

Has the use of zinc sulphate, given orally, shortened the time or complete
healing? What other factors should be considered in the design of this
experiment?
(b)   The ages in months at which samples of 8 boys and 6 girls learned to walk
were as follows:
Boys 14,        15,      16,     13,       13,    15,      14,      11
Girls 11,       14,      12,     12,       11,    15
Is there evidence to suggest the girls learned to walk at a significantly earlier
age than boys? What factors should be considered in choosing these
samples?                                                                    (10)
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ASSIGNMENT No. 2
(Units: 6–10)
Total Marks: 100                                                        Pass Marks: 40

Q. 1 (a)   In a psychological testing experiment, 25 subjects are selected randomly and
their reaction time, in seconds, to a particular experiment, is measured. Past
experience suggests that the variance in reaction time to these types of
stimuli is 4 sec2 and that reaction time is approximately normal. The average
time for the subjects was 6.2 seconds. Give an upper 95% bound for the
mean reaction time. Interpret.                                            (10)
(b)   A quality control supervisor for an automobile manufacture is concerned
with uniformity in the number of defects in cars coming off the assembly
line. If one assembly line has significantly more variability in the number of
defects, then changes have to be made. The supervisor has collected the
following data:
Number of Defects
Assembly Line A        Assembly Line B
Mean                          10                     11
Variance                         9                     25
Sample Size                      20                     16
Does the assembly line B have significantly more variability in the number
of defects? Test at 0.05 level of significance.                           (10)

Q. 2 (a)   In a trial of diabetic therapy, patients were either treated with Phenformin or
a placebo. The numbers of patients and deaths from cardiovascular causes
were as follows;
Treatment Group
Phenformin           Placebo          Total
Cardiovascular deaths                 26                 2               28
Not cardiovascular deaths            178                62              240
Total                                204                64              268
Do these data provide evidence of a difference in cardiovascular mortality
between the treatment groups?                                         (10)
(b)   In a randomized trial of difference regimes for the management of diabetes,
two of the groups received diet and tolbutamide and diet and placebo
respectively. At the end of the trail the results were:

Treatment                     Deaths          Survivors           Total
Tolbutamide                     30              174                204
Placebo                         21              184                205
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Estimate the death rates (%) in the two treatment groups, giving 95%
confidence of limits. Estimate the difference in the death rates, with 95%
confidence limits. Has the study shown a difference between the
treatments?                                                             (10)

Q. 3 (a)   A random sample of the records of a certain hospital yielded the following
information on the length of hospital stay in days and the annual family income
(rounded to the nearest \$ 500) of 15 discharged patients. Plot a scatter diagram
and calculate the linear regression equation and add it to the diagram.
Annual income, \$, (x) 2000 2500 3000 3500 4000 4500 5000 5500
Length of stay, days, (y) 11    12       9      8         9       10    7    8
Annual income, \$, (x) 6000 6500         700 7500 8000 8500 9000
Length of stay, days, (y) 4      7       5      6         3       4     4
To help with arithmetic in case you are doing it the hard way, i.e.
without a computer package:
 x  82 500;  x 2  523 750 000;  y  107;
y   2
 871;    xy  510 500.                                          (10)
(b)   Calculate the correlation coefficient for the above data and interpret your
results.                                                               (10)

Q. 4 Explain in detail the situations, where the non-parametric tests are applicable and
also describe their testing procedures in detail.                              (20)

Q. 5 (a)   We wish to carry out a study to rest whether the rate of asthma in children is
increased in those living downwind of a particular control group from other
parts of the district, where it is estimated that the rate is 2%. We wish to be
able to detect a doubling of the rate. How many children are needed in each
group or for the study?                                                    (10)
(b)   For a certain disease the mortality rate in five years after conventional
therapy is 45%. A clinical trial of a new therapy is to be carried out, and it is
considered that the new therapy would be useful if the mortality fell to 35%.
How many patients are required for the trail? If the researcher only has
resources to study 100 patients per group, what differences in mortality can
be the reasonably sure of detecting?                                       (10)

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