LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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M.Sc. DEGREE EXAMINATION – BIO.INST.SCI.& MED. LAB. TECHNOLOGY
THIRD SEMESTER – November 2008
ST 3901 – STATISTICAL APPLICATIONS IN BIOLOGICAL SCIENCES
Date : 14-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A (10 X 2 = 20 Marks )
Answer ALL the Questions. Each Carries TWO marks.
- Distinguish between a statistic and a parameter. Give an example for each.
- State any three properties of the arithmetic mean.
- The following are the serum lipid peroxide (SLP) values obtained from a sample of 10 apparently healthy adults :
4.07, 2.07, 3.64, 3.37, 3.84, 3.83, 3.82, 4.21, 4.04, 4.50.
For these data compute the mean, the variance and the standard deviation.
- What assumptions does one make when computing the following from grouped data? (a) The mean (b) The median (c) The variance.
- What is the purpose of the coefficient of variation ?
- Explain linear and non-linear correlation.
- What is meant by multiple regression analysis ?
- Discuss about 95 % confidence interval.
- Write any three applications of the Chi – Square test.
- Define the variance ratio ( F ) and write the name of the sampling distribution of F.
SECTION – B (5 X 8 = 40 Marks )
Answer any FIVE Questions. Each Carries EIGHT marks.
- The following are the fasting blood glucose levels of a sample of 10 children:
Value : 56, 62, 63, 65, 65, 65, 65, 68, 70, 72.
Compute ( a ) The mean ( b ) The median ( c ) The mode.
- The following table shows the age distribution of cases of a certain disease
reported during a year in a particular state.
Age : 5-14 15-24 25-34 35-44 45-54 55-64
No. of cases : 5 10 20 22 13 5
Compute the mean and standard deviation.
- Describe the scatter diagram method of studying correlation with illustrations.
- For the following data on RNA content ( X ) of cells and rate of protein synthesis ( Y ), calculate regression equation of Y on X.
RNA content (mg/100ml) : 40 45 48 54 66 78 86 90
Protein Synthesis rate (mg/hr) : 5.0 5.8 6.4 7.2 7.5 7.8 8.2 9.0
- In a survey on hearing level of school children with normal hearing it was found that in the frequency 500 cycles per second, 62 children tested in the sound proof room had a mean hearing threshold of 15.5 decibels with a standard deviation of 6.5. 76 comparable children who were tested in the fields had mean threshold of 20.0 decibels with a standard deviation of 7.1. Test if there is any difference between the hearing levels recorded in the sound proof room and in the field.
- The severity of a disease and blood type were studied. The findings are given
in the following table :
| Severity | Blood group | |
| O | Others | |
| Yes | 51 | 59 |
| No | 489 | 901 |
Test for the independence of the blood groups and the severity of the disease.
- State the assumptions of ANOVA.
- Calculate the rank correlation coefficient from the following data :
Price of Tea ( Rs.) : 75 88 95 70 60 80 81 50
Price of Coffee( Rs.) : 100 134 150 115 110 140 142 100
SECTION – C ( 2 X 20 = 40 Marks )
Answer any TWO Questions. Each Carries TWENTY marks.
- The following table shows the number of hours 45 hospital patients slept
following the administration of a certain anesthetic.
| 7 | 10 | 12 | 4 | 8 | 7 | 3 | 8 | 5 |
| 12 | 11 | 3 | 8 | 1 | 1 | 13 | 10 | 4 |
| 4 | 5 | 5 | 8 | 7 | 7 | 3 | 2 | 3 |
| 8 | 13 | 1 | 7 | 17 | 3 | 4 | 5 | 5 |
| 3 | 1 | 17 | 10 | 4 | 7 | 7 | 11 | 8 |
From these data construct :
( a ) A frequency distribution.
( b ) A relative frequency distribution.
( c ) A histogram.
( d ) A frequency polygon.
- ( a ). The first four central moments of a distribution are 0, 2.5, 0.7 and 18.75.
Test the skewness and kurtosis of the distribution. ( 5 )
( b ). Calculate Kelly’s Coefficient of skewness from the following positional
measures given below :
P90 = 205, P10 = 25, P50 = 150 ( 5 )
( c ). Calculate Karl Pearson’s coefficient of correlation for the following data
on length in cm ( X ) and weight in gm ( Y ) of a species of aquarium
fish.
X : 3 7 12 15 20 25 30
Y : 5 10 15 20 25 30 35 ( 10 )
- A health status survey in a few villages revealed that the normal serum
protein value of children in that locality is 7.0 g / 100 ml. A group of 16
children who received high protein food for a period of six months had serum
protein values shown below. Can we consider that the mean serum protein
level of those who were fed on high protein diet is different from that of the
general population ?
Protein Level ( g % ) 7.10, 7.70, 8.20, 7.56, 7.05, 7.08, 7.21 , 7.25, 7.36,
6.59, 6.85, 7.90, 7.27, 6.56, 7.93, 8.56 .
- The haemoglobin levels of three groups of children fed on three different
are given below. Test whether the means of these three groups differ
significantly.
Haemoglobin levels ( g % )
Group I Group II Group III
11.6 11.2 9.8
10.3 8.9 9.7
10.0 9.2 11.5
11.5 8.8 11.6
11.8 8.4 10.8
11.8 9.1 9.1
12.1 6.3 10.5
10.8 9.3 10.0
11.9 7.8 12.4
10.7 8.8 10.7
11.5 10.0
9.7
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