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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) 1 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 2 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) 3 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 4 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) 5