LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

           B.Sc. DEGREE EXAMINATION – ADV.ZOO.&BIOTE.&PLA.BIO.&BIOTEC.

NO 10

THIRD SEMESTER – APRIL 2008

ST 3203 / 3201 – BIOSTATISTICS

 

 

 

Date : 05/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer all questions                                                                      10 x 2 = 20

 

1. A sample of 15 patients making initial visits for a health department travelled the following distances in miles/second. 5,9,11, 3 , 12 , 13 , 12 , 6 , 13, 7 , 3 , 15 , 12 , 15 , 5. Find the median distance travelled.
2. Mention any two advantages of Standard deviation as a measure of Dispersion.
3. An unbiased coin is tossed 3 times. What is the probability of getting 2 heads?
4. What is meant by ‘ Standardised random Variable ‘? Mention its properties.
5. Define Simple random sampling.
6. Give the 100(1-a)% Confidence Interval for the difference between two population proportions.
7. What is meant by ‘Ordinal ‘ data? Give an example.
8. Define Analysis of variance.
9. Consider the following probability distribution

X:                    -1         3          5          7

P(X=x):           0.2       0.1       0.4       0.3

Find the variance of X

1. Mention any two advantages of t-distribution.

 

SECTION – B

Answer any FIVE questions                                                                          5 x 8 = 40

 

1. As part of research project, investigators obtained the following data on serum lipid peroxide (SLP) levels from laboratory reports of a sample of 10 adult subjects undergoing treatment for diabetes mellitus: 5.85 , 6.17 , 6.09 , 7.70 , 3.17, 3.83 , 5.17 , 4.31 , 3.09 , 5.24 . Compute the mean, median, variance and standard deviation.
2.  a) Mention any four properties of normal distribution.

15. b) The weights of a certain population of young adult females are approximately normally distributed with a mean of 132 pounds and a standard deviation of 15. Find the probability that a subject selected at random from this population will weigh: (i) More than 155 pounds

(ii) Between 105 and 145 pounds.

1.  a) What are sampling distributions? Mention its uses.

1. b) Explain the steps for constructing sampling distribution

1. A simple random sample of 16 apparently normal subjects yielded the following values of urine excreted arsenic ( milligrams per day )

Subject      1          2          3          4          5          6          7          8          9          10

Value         7          30        25        8          30        38        7          5          12        6

 

Subject      11        12        13        14        15        16

Value         10        32        6          9          14        11

Construct a 95% confidence interval for the population mean.

1. Explain the various steps involved in testing statistical hypothesis.

 

1. Complete the following ANOVA table and interpret the results.

Source             d.f.                  SS                    MSS                F-ratio

Treatments      3                      ?                      ?                      ?

Blocks             3                      183.5               ?                      ?

Error                ?                      26.0                 ?                      ?

Total                15                    709.0

1. Explain the concepts of correlation and regression with an example each.

 

 

 

1. The face sheet of patients’ records maintained in a local health department contains 10 entries. A sample of 100 records revealed the following distribution of erroneous entries.

Number of erroneous                          Number of records

Entries out of 10

• 8
• 25
• 32
• 24
• 10

5                                                          1

Test at 5% level the goodness-of-fit of these data to binomial distribution.

 

SECTION- C

Answer any TWO questions                                                              2 x 20 =40

 

1.  a) The following are the number of babies born during a year in 40 community hospitals.

30        55        27        45        56        48        45        49

37        55        52        34        54        42        32        59

32        26        40        28        53        54        29        42

39        56        59        58        49        53        30        53

52        57        43        46        54        31        22        31

(i) Using  Sturge’s rule, group the data into various class intervals and obtain the frequency distribution.

(ii) Compute the mean, median and mode of the number of babies born.

1. b) Define sample space, mutually exclusive events and independent events.

(14+6 )

1. a) An experiment was conducted to study the effect of a certain drug in lowering heart rate in adults. The independent variable is dosage in milligrams of the drug, and the dependent variable is the difference between lowest rate following administration of the drug and a predrug control. The following data were collected.

Dose(mg)                    Reduction in heart rate (beats/min)

X                                                       Y

• 10
• 8

• 12
  • 12
  • 14
  • 12
• 16
  • 18

Obtain the regression equation of Y on X.

1. b) Five hundred employees of a firm that manufactures a product suspected of being associated with respiratory disorders were cross-classified by level of exposure to the product and whether or not they exhibited symptoms of respiratory disorders. The results are shown in the following table:

 

Level of Exposure

Symptoms present       High                Limited           No known exposure

Yes                  185                  33                                17                                No                   120                  73                                72

Do these data provide sufficient evidence at 1% level, to indicate a relationship between level of exposure and the presence of respiratory disorder symptoms?                          (10 + 10)

1. a) Three groups of animals were used in an experiment to compare response time, in seconds, to three different stimuli. The following results were obtained.

Stimulus

I                       II                     III

16                    6                      8

14                    7                      10

14                    7                      9

13                    8                      10

13                    4                      6

12                    8                      7

12                    9                      10

17                    6                      9

 

Do these data provide sufficient evidence to indicate a difference among population means ?        Let a = 0.05.

1. b) Ten experimental animals were subjected to conditions stimulating disease. The number of heartbeats per minute, before and after the experiment were recorded as follows:

Animal              1        2          3          4          5          6          7          8          9          10

Before   70      84        88        110      105      100      110      67        79        86

After     115    148      176      191      158      178      179      140      161      157

Do these data provide sufficient evidence to indicate that the experimental condition increases the number of heartbeats per minute? Let a = 0.05.                                                              (10 + 10)

 

1. a) A researcher designed an experiment to assess the effects of prolonged inhalation of cadmium oxide. Fifteen laboratory animals served as experimental subjects, while ten similar animals served as controls. The variable of interest was hemoglobin level following the experiment. The results obtained are as shown below:

 

Exposed animals                     Unexposed animals

• 4
• 2
• 1
• 5
• 0
• 0
• 9
• 0
• 3
• 8

15.7

16.7

13.7

15.3

14.0

Use Mann-Whitney test to test whether the median hemoglobin level of the population of animals exposed to cadmium oxide is the same as that of animals not exposed to it. Use 5% level.

1. b) Explain the concept of Interval Estimation. (15 + 5)

 

 

 

Go To Main Page

 

 

 

 

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BA 06

   B.Sc. DEGREE EXAMINATION – ADV.ZOO. & BIO. TECH.

THIRD SEMESTER – November 2008

ST 3203 /ST 3201 – BIOSTATISTICS

 

 

 

Date : 13-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer all questions.                                                                        (10×2=20)

1. What is a frequency polygon?
2. Give the various measures of dispersion.
3. Define mutually exclusive events.
4. The probability distribution of a random variable ‘X’ is given below.

X:        0.5       1.2       2.4

P[X=x]:       1/3       1/5       7/15.  Find E(X).

5. Find the mean of the Poisson distribution for which P(X=1) = 2P(X=2).
6. Define sampling distribution.
7. From a random sample of 12 observations the mean and variance are found to be 27 and 3.2 respectively. Find the value of the test statistic for testing the hypothesis that the population mean is 30.
8. What is a contingency table?
9. Show that for a standardized random variable, the mean and variance are zero and one respectively.
10. Give an example for one way analysis of variance.

 

SECTION B

Answer any five questions.                                                         (5×8=40)

 

11. Calculate the quartile deviation based on the following data:

Blood pressure:70-74  75-79  80-84  85-89   90-94   95-99

                          No. of patients:   8         19        29        36        25        13              

12. The following are the weights (in kg’s) of 10 subjects who participated in a health camp.

83.9, 99.0, 63.8, 71.3, 65.3, 79.6, 70.3, 69.2, 56.4 and 66.2.

Examine the skewness of the above data by constructing a box plot.

13. The probability of A, B and C hitting a target is 0.25, 0.5 and 0.25 respectively. If all of them try independently, what is the probability that a.) the target will be hit ) any two of them will hit the target

c.) none of them will hit the target.

14. It is known that 35 percent of the members of a certain population suffer from one or more chronic diseases. What is the probability that in a sample of 200 subjects randomly drawn from this population, 1.) 80 or more will have atleast one chronic disease? ) between 30 and 60 will have atleast one chronic disease?
15. Obtain the sampling distribution of mean by taking all possible samples of size two without replacement based on the following population values.

13.5, 15.0, 17.7, 10.3, 14.1, 15.0

16. Explain the procedure for testing the equality of two population proportions.
17. Suppose a study to examine the relative efficacy of pencillin and spectinomycin in the treatment of gonorrhea is conducted. Three treatments are looked at (1) pencillin, (2) spectinomycin, low dose and       (3) spectinomycin, high dose. Three responses are recorded: (1) positive smear, (2) negative smear, positive culture and (3) negative smear, negative culture. The data obtained is given below:

     

                                                                         Response

Treatment            + smear      – smear, + culture      – smear, – culture

                     Pencillin                  40                     30                              130

                     Sceptinomycin        10                     20                               70

                     (low dose)

                     Sceptinomycin        15                     40                               45

                     (high dose)

             Test whether there is any relationship between the type of treatment and

the response. Use 5% level.

 

18. Fit a Poisson distribution to the following data.

Mistakes:   0     1     2     3      4      5.

No. of pages:  52    40  31   19     5      2

 

                                                           SECTION C

      Answer any two questions.                                                         (2×20=40)

  

19. ) The following scores represent a nurses’ assessment (X) and a physicians’ assessment (Y) of the

condition of 10 patients at a time of admission to a trauma care center.

X: 18   13   18   15   10   12   8     4   7   3

Y: 23   20   18   16   14   11  10    7   6   4

Calculate the Karl Pearson’s coefficient of correlation between X and
Y. Interpret your answer.

b.) Assume that a factory has two machines. Past records show that
machine 1 produces 45 % of the items of the output and machine 2

produces 55 %. Further 3 % of the items produced by machine 1 were
defective and only 1% produced by machine 2 were defective. If a
defective item is drawn at random, what is the probability that it was
produced by a.) machine 1  b.) machine 2?                               (12+8)

20. a.) It is known that 30 percent of a certain population is immune to some
    disease. If a random sample of size 10 is selected from this
    population, what is the probability that it will contain a.) exactly four
    immune persons  b.) less than two immune persons and   c.) more
    than eight immune persons.

b.)  Transverse diameter measurements (in cm’s) on the hearts of adult

males and females gave the following results:

Group          Sample size         Sample mean    Sample SD

Males                 12                        13.21                1.05

Females                  9                         11.00                 1.01

Assuming normally distributed populations with equal variances,
construct the 95 and 99 percent confidence intervals for the
difference between the population means.

c.)  Mention any four properties of normal distribution.                            (8+8+4)

 

21. a.) The following PaO₂ measurements were obtained before and after
    the inhalation of methacholine (MTH) in 10 patients with asthma.

Patient:    1        2       3       4         5         6        7         8        9     10

Before: 88.2  100.9  96.0   99.1   86.9   103.7   76.0   81.8   72.1  93.7

After: 70.6    70.0  71.0   64.1   79.5    79.5    72.2   70.6   66.9  67.0

Do these data provide sufficient evidence to indicate that MTH cause

a decrease in PaO₂. Let α = 0.05.

b.) Explain the median test for testing the equality of median of two
independent populations.                                                          (10+10)

22. The following table gives the time (in days) required by a set of patients
    classified by age group to learn the use of a certain prosthetic device by
    three different teaching methods.

Teaching Method

Age group       A         B         C

Under 20         7          9          10

20 – 29            8          9          10

30 – 39            9          9          12

40 – 49            10        9          12

50 and above   11        12        14

Perform a two way analysis of variance by clearly stating the hypothesis.

 

 

Go To Main Page