# Loyola College B.Sc. Plant Biology and Biotechnology April 2009 Biostatistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PLANT BIOLOGY & BIOTECHNOLOGY

 YB 10

THIRD SEMESTER – April 2009

# ST 3203 / 3201 – BIOSTATISTICS

Date & Time: 16/04/2009 / 1:00 – 4:00         Dept. No.                                                       Max. : 100 Marks

SECTION A

Answer all questions.                                                                        (10 x 2 = 20)

1. What is meant by quantitative and qualitative data?
2. Mention any two properties of arithmetic mean.
3. Define: Independent events.
4. Let A, B and C be three mutually exclusive and exhaustive events with           P(A) = P(B) / 2 , P(B) = 3 P(C) . Find P(A), P(B) and P(C).
5. What is the probability of obtaining three heads in a toss of four unbiased coins?
6. Let X be a random variable with the following probability distribution

X:        -1         0          1          2

P[X=x]:        0.3       0.2       0.2       0.3

Find the distribution of Y = X2.

1. Mention any two uses of t-distribution.
2. Define the term ‘Statistic’.
3. Interpret the following confidence interval:

Pr(1.2 < μ < 2.7) = 0.99

1. What are Type 1 error and Type II error?

SECTION B

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

1. Calculate mean, median and mode for the following data

Weight: 50-55    55-60    60-65    65-70    70-75    75-80

No. of patients:    10          8           14          9           5            2

1. Explain the concept of correlation and regression with an example each.
2. Let X be a normally distributed random variable with mean 57 and variance 20. Find   a) P(X>62)
1. b) P(42<X<50)
2. c) P(X< 70)
1. Explain the various steps involved in hypothesis testing.
2. The following data gives the age of 10 randomly chosen patients admitted in the intensive care unit of a hospital in a given week.

40, 52, 48, 63, 37, 24, 49, 58, 69, 75.

Can it be concluded, based on the above information, that the mean age of

all the patients admitted in the given week is more than 55? Test at 5 %  level.

1. Of the 215 subjects who were black, 58 had diabetes mellitus. Of the 1140 white subjects, 217 had diabetes mellitus. Construct a 90 % confidence interval for the difference between the two population proportions. What are the relevant population proportions?
2. Explain the Mann – Whitney test to test the equality of median of two populations.
3. Fit a binomial distribution to the following frequency distribution.

X:        0          1          2          3          4

f:        12        15        18        14        10

SECTION C

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

1. a.) Draw a Box – Plot and examine the Skewness of the following
frequency  distribution:

No. of children per family:     0          1          2          3          4          5         6                                                     No. of families:           7          10        16        25        18        11       8

b.) The following data gives the Blood Pressure (Y) and age (X) of 10
patients:

Y:        78        64        89        94        88        72        90        82

X:        28        45        52        49        37        41        56        24

Fit a linear regression of Y on X and obtain the least square estimates of
the intercept and slope parameters. Also interpret the results     (8+12)

1. a.) The following data (Sample A and Sample B)denotes the age (in

months) at which infants walked alone from two populations A and B.

Sample A:       9.5       10.5     9.0       9.75     10.0     13.0     10.0                                                     13.5      10.0     9.5       10.0     9.75

Sample B:        12.5     9.5       13.5     13.75   12.0     13.75   12.5                                                     9.5      12.0     13.5     12.0     12.0

Do the above sample data support the hypothesis that the mean age at
which the infants walked alone is different in the two populations? Test

at 5% level.

b.) Consider a population with N=6 units, the values being 30, 22, 20, 15,

24 and 20. Select all possible samples of size 2 without replacement

and verify whether the sample range is an unbiased estimator for the

population range.                                                                        (12+8)

1. ) A sample of college students participated in a study designed to

evaluate the level of college students’ knowledge of a certain group of

common diseases. The following table shows the students classified by

their major field of study and level of knowledge of the group of

diseases.

Knowledge of Diseases

Major               Good               Average           Poor

Premedical      85                    58                    30

Other               19                    29                    48

Do these data suggest that there is a relationship between knowledge of
the group of diseases and major field of study? Test at 5 % level.

b.) Draw a histogram and a frequency polygon for the following frequency
distribution.

Class Interval: 10-19   20-29   30-39   40-49   50-59   60-69

frequency:     4         66        47         36        12        4      (12+8)

1. A remotivation team in a psychiatric hospital conducted an experiment to
compare five methods for remotivating patients. Patients were grouped
according to the level of initial motivation. The team assigned each patient
a composite score as a measure of his or her level of initial motivation. The
results were as follows:

Remotivation method

Level of initial motivation      A         B         C         D         E

Nil                   58        68        60        68        64

Very low         62        70        65        80        69

Low                 67        78        68        81        70

Average           70        81        70        89        74

Do these data provide sufficient evidence to indicate a (i) difference in

mean scores among methods and (ii) mean scores among level of initial

motivation? Test at 5 % level.

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