Seat No.:
Subject Code: 220001
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Enrolment No.
GUJARAT TECHNOLOGICAL UNIVERSITY
B.Ph. - SEMESTER- II EXAMINATION - WINTER-2017
Subject Name: Applied Mathematics (Biostatistics)
Time: 02:30PM TO 05:30PM
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Date: 28/12/2017
Total Marks: 80
Instructions:
- Attempt any five questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) A Beer’s law plot is constructed by plotting ultraviolet absorbance vs. concentration, with the following result:
Concentration (X) | 1 | 2 | 3 | 4 | 5 | 6 | 7
Absorbance (y) | 0.125 | 0.24 | 0.368 | 0.547 | 0.697 | 0.785 | 0.854
i) Calculate slope and intercept
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ii) An unknown has an absorbance of 6.65. What is the concentration?
(b) Define regression coefficients and state their properties.
(c) A population consists of 6 units with values 3, 2, 1, 4, 6, 5. Write down all possible samples of size 2 with and without replacement and find sample mean for each sample.
Q.2 (a) What is correlation? Distinguish between positive, negative and zero correlation.
(b) Explain sampling methods.
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(c) Explain Chi-square test with equation.
Q.3 (a) Explain the following terms:
Hypothesis, Statistical hypothesis, Null hypothesis, Alternative hypothesis, Test of a hypothesis, Critical region, Types of errors in testing of a hypothesis, Level of significance
(b) Explain two-way analysis of variance.
(c) It is suspected that four methods of analysis in the laboratory are not accurate. A known sample is analyzed using each method and replicate assays performed each with the following results:
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Method A | Method B | Method C | Method D
10 | 9 | 8 | 9
11 | 10 | 8 | 9
10 | 11 | 8 | 9
By applying one-way ANOVA, test whether the mean assay is the same for the four different methods of analysis. F at 5 % level = 4.07
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Q.4 (a) Explain F-test for equality of two variances.
(b) Explain ANOVA and state some applications of analysis of variance.
Q.5 (a) Write in detail factors for designing clinical studies.
(b) Explain the following terms with reference to experimental designs in clinical trials:
i) Wash out period ii) Carry over effect iii) Replicate design iv) Crossover
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(c) What is a crossover design? Discuss merits and demerits of crossover design.
Q.6 (a) Enumerate the experimental designs in clinical trials? Discuss in detail about any one experimental design.
(b) Write note on followings:
i) Wilcoxon signed rank test ii) Kruskal wallis test iii) Wilcoxon rank sum test.
(c) Explain in detail Rank test.
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Q.7 (a) A random sample of 20 tablets from a batch gives a mean ingredient content of 42 mg and a standard deviation of 6 mg. Test the hypothesis that the population mean is 44 mg (t at 5 % level of significance = 2.093)
(b) What do you mean by biostatistics? Explain its importance in Pharmacy.
(c) What are the advantages and disadvantages of nonparametric tests
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