NO 47

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – BIO INST & MED.LAB TECH

THIRD SEMESTER – APRIL 2008

         ST 3901 – STATISTICAL APPLICATIONS IN BIOLOGICAL SCIENCES

 

 

 

Date : 05-05-08                  Dept. No.                                        Max. : 100 Marks

   Time : 9:00 – 12:00

PART A

Answer all the questions.                                                                  5 X 2 = 10

1. Define biostatistics.
2. What are the merits of arithmetic mean?
3. What measures are available in measure of dispersion?
4. Define correlation.
5. Write any two properties of regression.
6. What is population and sample?
7. What do you mean about two-sample t-test in health science?
8. What is analysis of variance?
9. Distinguish between  sampling error and non-sampling error.

10. Explain simple random sampling by illustration.

PART B

Answer any FIVE questions.                                                                       5 X 8 = 40

 

1. Compute mean and median for the following data:

Age                 : 20-30   30-40   40-50   50-60   60-70   70-80   80-90

Number of patients     :    15        19        11          25        22        10         5

1. Calculate correlation coefficient for weights (kg) and heights (cm)  of  10 patients in Seahorse hospital.

Weight :  83    99       63       71       65       70       69       56       66       88

Height  : 185   180      173      168      175      183      174      164      169      205

 

1. The following data are the oxygen uptakes (milliliters) during incubation of a random sample of 15 cell suspensions.

14.0     14.1     14.5     13.2     11.2     14.0     14.1     12.2     11.1     13.7     13.2

16.0     12.8     14.4     12.9

Do these data provide sufficient evidence at the 0.05 level of significance that the population mean is not 12ml?

 

1. Cortisol level determinations were made on two samples of women at childbirth. Group 1 subjects underwent emergency cesarean section following induced labor. Group 2 subjects delivered by either cesarean section or the vaginal route following spontaneous labor. The sample sizes, mean cortisol levels, and standard deviations were as follows:

Sample                        n          mean    standard deviation

1                 10            435              65

2                 12            645              80

Use two sample t-test to provide sufficient evidence to indicate a difference in the

mean cortisol level in the populations represented? Let a = 0.05.

 

1. Explain any four methods of sampling and give example for each.

 

1. Four subjects participated in an experiment to compare three methods of relieving stress. Each subject was placed in a stressful situation on three different occasions. Each time a different method for reducing stress was used with the subject. The response variable is the amount of decrease in stress level as measured before and after treatment application. The results were as follows.

Subject	Treatment
	A	B	C
1	16	26	22
2	16	20	23
3	17	21	22
4	28	29	36

Can we conclude from these data that the three methods differ in effectiveness? Let a = 0.05.

17. Explain various steps in involved in Hypothesis testing.
18. Explain any four important measures of dispersion.

 

PART C

Answer any two questions.                                                                2 X 20 = 40

 

1. The following are the number of babies born during a year in 60 community hospitals.

30        55        27        45        56        48        45        49        32        57        47        56        37        55            52        34        54        42        32        59        35        46        24        57        32        26        40        28            53        54        29        42        42        54        53        59        39        56        59        58        49        53            30        53        21        34        28        50        52        57        43        46        54        31        22        31            24        24        57        29        2          18        25        6          9          15        23        46        11        22

From these data construct:

a). A frequency distribution with the class interval 0-10, 10-20, 20-30, 30-40,

40-50, 50-60

b). Histogram.

c). Frequency polygon.

d). Frequency curve

 

1. Consider the following Bivariate data:

X:  3.31  2.41   2.11  3.01  2.13  2.41  2.10  2.41  2.09  3.00

 

Y: 4.09  3.84   2.97  3.22  3.96  2.76  3.42  3.38  3.28  2.93

a). Find two regression equations describing the relationship between the two

variables.

b). Compute r² and give your interpretation.

c). Estimate X when Y = 2.00 and Y when X = 2.80.

 

1. [i] The Weights (in Kg.) of  9 Obese Women before and after 12-weeks of

VLCD (very low calorie diet) treatment  are given in following table. Test whether

these data provide sufficient evidence to allow us to conclude that the treatment is

effective in causing weight reduction in obese women? Let a=0.05

Before  : 117.3    114.4      98.6    104.3   105.4   100.4   81.7   89.5   78.2

After    :  83.8      85.9        75.8    82.9     82.3      77.7    62.7   69.0   63.9

[ii] In a study of nutrition care , it is found that among 55 patients with hypertension, 24 were on sodium-restricted diet. Of 149 patients without hypertension, 36 were on sodium-restricted diets. May we conclude that the proportion of patients on sodium-restricted diet is higher among patients with hypertension than among patients without hypertension?

 

1. A physical therapist wished to compare three methods teaching for patients to use a certain prosthetic device. He felt that the rate of learning would be different for patients of different ages and wished to design an experiment in which the influence of age could be taken into account.

 

Age Group	Teaching Method
Under 20	A	B	C
	7	9	10
20 to 29	8	9	10
30 to 39	9	9	12
40 to 49	10	9	12
50 and over	11	12	14

 

Use two-way analysis of variance for a = 5 % level and give your interpretation.

 

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BA 28

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.

 

1. Distinguish between a statistic and a parameter.  Give an example for each.
2. State any three properties of the arithmetic mean.
3. 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.

1. What assumptions does one make when computing the following from grouped data?   (a) The mean (b) The median (c) The variance.
2. What is the purpose of the coefficient of variation ?
3. Explain linear and non-linear correlation.
4. What is meant by multiple regression analysis ?
5. Discuss about 95 % confidence interval.
6. Write any three applications of the Chi – Square test.
7. 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.

 

1. 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.

 

1. 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.

 

1. Describe the scatter diagram method of studying correlation with illustrations.

 

1. 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

 

1. 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.

 

1. 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.

 

1. State the assumptions of ANOVA.

 

1.  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.

 

1. 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.

 

1. ( 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 )

 

21. 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 .

 

22. 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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