LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – ADV.ZOOL. & PL.BIO.&BIOTECH.

AC 09

THIRD SEMESTER – APRIL 2007

ST 3201 – BIOSTATISTICS

 

 

 

Date & Time: 04/05/2007 / 9:00 – 12:00 Dept. No.                                              Max. : 100 Marks

 

 

SECTION A

Answer all questions.                                                                        (10×2=20)

 

1. Mention the advantages of diagrammatic representation of data.
2. Give any two limitations of geometric mean.
3. What is meant by Skewness? Mention any one method of identifying the same.
4. Find the 70^th percentile of the following series :

49,52,12,87,62,35,21,19.

1. Define: Independent events.
2. Let A, B and C be three mutually exclusive and exhaustive events and exhaustive with

P( A ) = P( B ) / 2 , P( B ) = 3 P( C ) . Find P (A), P( B ) and P( C ).

1. Comment on the following statement: “For a binomial distribution, the mean and variance are found to be 5 and 10 respectively “
2. Define: ‘Parameter’.
3. Mention any two uses of t-distribution.
4. What is the need for non-parametric tests?

 

SECTION B

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

 

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

Hourly wages(Rs):     66-68   68-70   70-72   72-74   74-76   76-78

No. of persons:          15       24        40        20        14        11

1. Write short notes on: i.) Standard deviation ii.) Quartile deviation.
2. a.) A group consists of 100 men and 80 women out of which 40 men and 50 women are graduates.

If one person is selected at random from the group, find the probability that the person is either

a woman or a graduate.

b.) A bag contains 5 white and 3 black balls. Two balls are drawn at random. Find the probability

that

1. i) One is white and the other is black
2. ii) Both are black

1. The probability that a student having a recommended book for study is 0.8. Three students are selected at random from a large group of students.

• Find the probability distribution of the number of students having the book
• Calculate the mean and variance of the distribution.

1. Let X be a normally distributed random variable with mean 14 and variance 20. Find   a ) P(X>18)

1. b) P(12<X<16)
2. c) P(X< 20)

1. Write short notes on:

1. Type I and Type II errors.
2. Steps involved in testing of a hypothesis

 

 

 

 

1. The wages of 10 workers selected at random from a factory are given below:

Wages ( In Rs ) : 578  572  570  568  572  578  570  572  596  584

Is it possible that the mean wage of all workers of this factory is Rs.580? Test at 5% level.

1. Explain Wilcoxon test to test the equality of median of two populations.

 

SECTION C

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

 

1. a.) Find the geometric mean for the data given below:

Marks:      4-8   8-12  12-16 16-20  20-24  24-28.

Frequency:         6     10       18       30       15        12

b.) Use Box – Plot to 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

c.)  What are percentiles? How are they interpreted?                     (8+8+4)

1. a.)  i.)Give axiomatic and relative frequency definition of probability.

ii.)State the addition rule of Probability.

iii.) Define conditional Probability

b.) The screws produced by a certain machine were checked by examining

samples each  of size  12. The following table shows the distribution of 128 samples according to the number of defective items they contain.

No.of Defectives	0	1	2	3	4	5	6	7
No.of Samples	7	6	19	35	30	23	7	1

Fit a binomial distribution and find the expected frequencies

1. Given P(X=1) = P( X=2) , where X~ Poisson ( λ ), find P ( X=3 )                       (8+8+4)

.

1. a.) In one section of a large city, 200 out of 250 residents have Myopia. In another section, , 120

out of 200 residents have the same. Using 5% level of significance, could it be concluded that

there is no difference between these two sections of the city in terms of Myopia.

b.) The following data present the yields in quintals of wheat taken randomly from two

agricultural plots of equal area.

Plot 1:  6.2       5.7       6.5       6.0       6.3       5.8       5.7       6.0       6.0                               5.8

Plot 2:  5.6       5.9       5.6       5.7       5.8       5.7       6.0       5.5       5.7                               5.5

Test the equality of variance of yields from these agricultural plots at 5% level.                  (8+12)

 

 

 

1. a.) Let X and Y denote the  times in hours per week that students in two

different schools watch television. Let F(x) and G(y) denote the   respective distribution functions. Use runs test to test the hypothesis

H₀: F(x) = G(y) Vs H₁: F(x) < G(y) at 5% level, using the following random sample of 10 observations from each school.

X:        16.75   19.25   22.00   20.50   22.50   15.50   17.25   20.75   18.60   21.30

Y:        24.75   21.50   19.75   17.50   22.75   23.50   13.00   19.00   16.45   15.50

b.) Consider a population with N=6 units, the values being 20,30,22,20,11,14. Select all

possible samples of size 2 and verify whether the sample range is an unbiased estimator for

the population range.                                                                                         (12+8).

 

 

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