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                     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – BIOMED.INSTR.&MED.LABO.TECHNO.

AB 29

THIRD SEMESTER – NOV 2006

           ST 3901 – STATISTICAL APPLICATIONS IN BIOLOGICAL SCIENCES

 

 

Date & Time : 03-11-2006/9.00-12.00      Dept. No.                                                    Max. : 100 Marks

 

 

Part A

Answer all the questions.                                                                            10 X 2 = 20

 

1. Define statistics.
2.  What are the advantages of diagrammatic presentation of data?
3. State the various measures of central tendency.
4. Define dispersion.
5. What do you understand by skewness and kurtosis?
6. Explain the meaning and significance of the concept of correlation.
7. Define statistic and parameter.
8. What is type II error?
9. Write any two uses of chi-square test.
10. What is analysis of variance?

PART -B

Answer any five questions.                                                                           5 X 8 = 40

 

1. Briefly explain the  scope, limitation and misuse of statistics.
2. The following data relate to the monthly expenditure ( in rupees) of the families A and B:

Items of expenditure                           Family A         Family B

Food                                                    1600                1200

Clothing                                              800                  600

Rent                                                    600                  500

Light and Fuel                                                200                 100

Miscellaneous                                      800                  600

Represent the above data by a suitable percentage diagram.

1. Calculate mean, median and standard deviation for the following data:

Age                 :           10-20   20-30   30-40   40-50   50-60   60-70

No. of death by HIV:    2          6          10        7           4          1

14.  Calculate Spearman’s coefficient of correlation between height and weight are given below:

Age     :           2          5          8          10        12        18        20        25

Weight:           4          8          15        28        32        45        50        60

 

1. In a random sample of 1000 persons from city Trichy, 400 are found to be consumers of Hans. In a sample of 800 from city Tanjore , 400 are found to be consumers of tobacco. Do these data reveal a significant difference between city Trichy and Tanjore, so far as the proportion of tobacco is concerned?

 

 

1. The following table shows the ages (X) and blood pressure (Y) of 8 persons.

X:        52        63        45        36        72        65        47        25

Y:        62        53        51        25        79        43        60        33

Obtain the regression equation of Y on X and find the expected blood pressure fo a person who is 49 years old.

1. 500 apples are taken at random from a large basket and 50 are found to be bad. Estimate the proportion of bad apples in the basket and assign limits within which the percentage most probably lies.
2. From the following table find is there any significance difference between treatments or not.

Treatment	Treatment1	Treatment2	Treatment3	Treatment4
Kumar Senthil Saravanan	80 70 68	100 88 99	110 96 79	70 85 94

PART C

Answer any two questions.                                                                         2 X 20 = 40

 

1. Explain different types of diagrams in statistics with an illustration.
2. For a random sample of 10 persons, fed on diet A, the increased weight in pounds in a certain period were:

10        6          16        17        13        12        8          14        15        9

For another random sample of 12 persons, fed on diet B, the increase in same period were:

7          13        22        15        12        14        18        8          21        23        10    17

Test whether the diets A and B differ significantly as regards their effect on increase in weight.

Given the following data:

Degrees of freedom    :          19       20       21       22       23

Values of t at 5 % level:          2.09     2.09     2.08     2.07     2.07

 

1. a). A certain drug is claimed to be effective in curing cold. In an experiment on 1000 persons with cold, out of which 250 were given the drug and 250 were given sugar pills. The patients reactions to the treatment are recorded in the following table:

 

Medicine         helped             harmed                        no effect          total

Drug                150                  30                    70                    250

Sugar pills       130                  40                    80                    250

On the basis of the data can it be concluded that there is a significant difference in

the effect of the drug  and sugar pills?

b). The average life span  of people in  Trichy district is 65 years with the

standard deviation of 4 years. Randomly 10 people were observed and their life

span were recorded:

45        60        75        72        68        63        65        68        70        71

Verify that is there any significance at 5 % level of signifance.

 

1. Four students were selected randomly from II M.Sc medical lab technology and they were given by different types of medicine for curing viral fever. The following hours have been taken by the medicine to cure the diseases.

Student           medicine1       medicine2       medicine3       medicine4

      Senthil            0.30                 0.35                 0.40                 0.45

Ishwariya       0.50                 0.55                 0.46                 0.48

Kannan          0.10                 0.20                 0.25                 0.29

Sona                0.50                 0.40                 0.45                 0.30

Is there any significance difference between medicines and students for taking

hours to cure the disease?

 

 

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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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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MEDICAL LAB TECHNOLOGY

THIRD SEMESTER – NOVEMBER 2012

ST 3901 – STATISTICAL APPLICATIONS IN BIOLOGICAL SCIENCES

 

 

Date : 08/11/2012            Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A

Answer ALL questions:                                                                                                       (10 x 2 = 20)

 

1. Define Correlation.
2. Give the various measures of dispersion.
3. What are the limitations of Statistics?
4. Explain type II error.
5. Write the test statistic for a chi-square test of independence of attributes.
6. Define ANOVA.
7. Find Range and coefficient of Range from the given data:

99, 77, 39, 89, 69, 79, 89, 99, 999, 899, 696, 969.

8. State any two uses of Regression.
9. Give the formula for Z-test for single proportion.
10. Give two way ANOVA table.

SECTION – B

Answer any FIVE of the following:                                                                                    (5 X 8 = 40)

 

11. Determine Karl Pearson coefficient of correlation for the following data

 

Drug taken(In days)	1	2	1	3	5	8	10	7
% Reduction of tumor	46	63	56	40	66	76	83	70

 

 

 

 

 

 

12. Explain the procedure of One Way ANOVA.

 

13. Given:

30, 71, 90, 86, 113, 40, 70, 10, 33, 20, 55

Calculate Mean, Median, Mode, and Quartile Deviation, Range from the above data.

 

14. Two diets are compared by conducting an experiment on two sets of 70 and 90 experimental animals. The average increase in weight due to the diet A and B are respectively 10 kg and 5 kg with standard deviation of 1 kg and 2 kg. Check the claim that diet B is superior over diet A at 5% level of significance.

 

 

 

 

15. Suppose we want to see the effect of a drug on blood pressure. Eight subjects are chosen and the blood pressure is measured for each subject before and after the administration of the drug. The result is shown below:

B.P before	119	114	129	125	137	131	141	131
B.P After	128	122	137	132	139	133	142	132

 

 

 

 

 

Does the drug has significant effect on blood pressure?

 

16. Calculate first four moments and kurtosis form the given data:

 

X	1	2	3	4	5	6	7
F	2	5	12	20	25	20	8

 

 

 

 

17. The following table gives the number of accidents that occurred during the various days of the week.

Days	Sun	Mon	Tue	Wed	Thu	Fri	Sat
No. Of accidents	14	16	8	20	11	9	14

 

 

 

Test whether the accidents are uniformly distributed over the week.

 

18. Eight Week wages (in thousands) for family A and B is given below:

FamilyA	6	3	4	7	5	8	9	6
Family B	9	10	1	3	7	14	2	8

 

Identify which family is more consistent.

 

SECTION – C

Answer any TWO of the following:                                                                                    (2 X 20 = 40)

 

19. To study the performance of four detergents and three different water temperatures, the following

‘Whiteness’ readings were obtained with specially designed equipment.

 

Water Temp.	Detergents     A               B                  C             D
Cold water	55	60	65	50
Warm water	50	56	50	65
Hot water	53	49	57	63

 

 

 

 

 

 

Perform a Two-way ANOVA, using 5% level of significance.                    (20)

 

 

 

 

 

20. (i) Calculate Karl Pearson’s coefficient of Skewness from the given data :    (10)

Age (X)	1	3	4	3	2	5	6	2
No. of childs (f)	7	9	11	14	6	4	12	10

 

 

 

 

 

 

(ii) Explain various types of diagrams for the present the data and also uses of statistics (10)

21. (i) Below are given the gain in weight in kgs of cows fed on two diets X and Y:

Diet X	35	42	40	42	34	24	42
Diet Y	34	44	32	40	52	41	50	40	42	45

 

 

 

 

Test at 5 % level whether the two diets differ as regards their effect on mean increase in weight by using t-test for difference means.                                                                   (10)

(ii) A certain drug is claimed to be effective in curing cold. In an experiment on 170

people with cold, half of them were given the drug and half of them given sugar pills.

The patient’s reaction to the treatment is recorded in the following table:

 

	Helped	Harmed	No effect
Drug	55	24	45
Sugar pills	43	15	35

 

Test the hypothesis that the drug is no better than sugar pills for curing cold.          (10)

22. (i) For the following data on RNA content of cells and rate of protein synthesis is given below:

RNA content (Mg/100 ml) X	40	45	48	54	66	78	86	90	95	100
Protein synthesis rate(Mg/hr) Y	5	6	7	7	8	7	9	10	11	10

 

 

 

 

 

 

Construct Regression Equation and also Estimate Protein synthesis rate when RNA content is       60 Mg/100 ml.                                                                                          (10)

(ii) Seven competitors in a beauty contest are ranked by three judges in the following orders:

 

1st Judge	2	3	1	6	5	7	4
2nd Judge	3	5	7	2	6	4	1
3rd Judge	6	4	5	1	3	7	2

 

 

 

 

 

Use the rank correlation coefficient to determine which pair of judges has the nearest approach       to common taste in beauty.                                                                                  (10)

 

 

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