LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

# 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.
1. 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)

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