1594-Statistical Methods in Environmental Health_VUsolutions.com by vufellows


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


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)

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

           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
     (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)
                             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
           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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