Gujarat Technological University 2009-2nd Sem B.Pharm B.E -(Applied Mathematics) - Question Paper
GUJARAT TECHNOLOGICAL UNIVERSITY
B. Pharmacy Sem-II examination June 2009
Subject Name: Applied Mathematics (Biostatistics) Time : 11:30am-2:30pm Total Marks: 80Subject code: (220001) Date : 08/06/09
Instructions:
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q-1
A
B
04
05
C
04
What is correlation? Distinguish between positive, negative and zero correlation. | ||||||||||||||||||||||
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i) Find the correlation coefficient between age and blood pressure. ii) Determine least square regression equation of blood pressure on age Estimate the blood pressure of women whose age is 45 years. A Beers law plot is constructed by plotting ultraviolet absorbance vs. concentration, with following result:_ |
Concentration ( x) |
1 |
2 |
3 |
5 |
10 |
Absorbance ( y) |
0.10 |
0.36 |
0.57 |
1.09 |
2.05 |
XY |
0.10 |
0.72 |
1.71 |
5.14 |
20.50 |
i) Calculate slop and intercept
ii) An unknown has an absorbance of 1.65. What is the concentration?
D Obtain the rank correlation coefficient between Fasting blood glucose level and systolic 03
blood pressure in 10 diabetic patients. | |||||||||||||||||||||||||||||||||
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Q-2 A What is analysis of variance? 01
C Eight laboratories were requested to participate in experiment whose objective was to 07 compare the dissolution rates of two generic products and standard product. The purpose of the experiment was to determine.
i) If the product had different rates of dissolution.
ii) To estimate the laboratory variability and test for significance difference among laboratories. Carry out two-way ANOVA for the given data and give your conclusion
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( From the F distribution table- F 2,14= 3.74,F7,24=2.43 and F14 ,24= 2.13 at 5%level of significance ) |
D The hemoglobin level of three group of children fed on three different diets are given in 05
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( From F distribution table F2,30 = 3.32 at 5%level of significance |
Q-3 A Explain the following terms related to testing of hypothesis. 04
i) Null hypothesis
ii) Alternate hypothesis
iii) Level of significance
iv) Standard error.
B A clinical research center of Zydus Cadila pharmaceutical conducted a pharmacokinetic 06 study in 12 human volunteer. The maximum therapeutic concentration of drug in plasma(C max) was studied after administration of new formulation and established formulation.
06
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Test whether there is statistical significance of difference between the two formulations. (t n,0.05=2.20 at 5% significance level) C The following data shows the blood pressure reduction (in mmHg) caused in 10 animal by a new antihypertensive compound. Test the hypothesis that blood pressure reduction for population in 15 mm Hg. (t9,0.05=2.262 at 5% significance level) |
Blood pressure |
1 5 |
18 |
14 |
8 |
90 |
12 |
17 |
21 |
16 |
18 |
reduction (mm Hg.) |
08
B
08
Q-5
A
B
C
04 03
05
Q-4 A Enumerate the experimental designs in clinical trials? Discuss in detail about any one experimental design.
Explain following terms with reference to experimental designs in clinical trials. i) Wash out period ii) Carry over effect
iii) Replicate design iv) Crossover Design
What is type I and type II errors.
Discuss in brief chi square test or goodness of fit.
Two granulation were prepared by different procedure Seven different random samples of powdered mix of equal weight ( equal to weight Of Final Dosage from) were collected from each batch and assayed for active pharmaceutical ingredient. The test is to be performed at the 5% level. (From F distribution table F 6,0.05=5.8)
Granulation A |
20.6 |
20.9 |
20.6 |
20.7 |
19.8 |
20.4 |
21.0 |
Granulation B |
20.2 |
21.5 |
18.9 |
19.0 |
21.8 |
20.4 |
21.0 |
D A certain drug is claimed to be effective in curing colds. In experiment on 500 person 04 with cold, half of them were given the drug and half of them were given sugar pill. The
patients reaction to the treatment is recorded in following table. On the basis of these data conclude that there is significance difference in the effect of drug and sugar pill. The test is to be performed at the 5% level
(Critical value of Chi square x 2 = 5.99 at 2 d.f.)_
Treatment |
Consequence | |||
Helped |
Reaction |
No effect |
Total | |
Drug |
150 |
30 |
70 |
250 |
Sugar pill |
130 |
40 |
80 |
250 |
Total |
230 |
70 |
150 |
500 |
E Enumerated the various methods of sampling and discuss in detail about any two 08 methods with suitable examples.
What are the advantages of and characteristics of the sample? 03
B
C
D
Q-7 A B
C
D
Differentiate between the sampling with replacement and without replacement 02
A population consists of five numbers 2,3,6,8.11. consider all possible size of two which can be drawn with replacement from this population. Calculate the standard error of sample mean
03
03 06
04
What arte the advantages of nonparametric tests Write note on followings ( any two )
i) Wilcoxon signed rank test ii) Kruskal wallis test iii) Wilcoxon rank sum test.
A Bioavailability study was conducted in which two products were compared ( A and B formulation ) . The peak blood concentrations were as follows; Use Wilcoxon signed rank test to determine if there is a difference among formulation. (Critical value for T at P= 0.05 for 12 pairs from table = 11)
03
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thoroughly investigated. One characteristic measures was diastolic blood pressure (mmHg).Is there any reason to believe that the 3 groups differ with these characteristics? |
( Table value of x 2 5.99 at d. |
\=k-1=2 and alpha = 0.05) | |||||
Group A |
100 |
103 |
89 |
78 |
105 | |
Group B |
92 |
97 |
88 |
84 |
90 |
95 |
Group C |
81 |
102 |
86 |
83 |
99 |
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Attachment: |
Earning: Approval pending. |