# Loyola College B.Sc. Plant Biology and Biotechnology Nov 2006 Biostatistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PLANT BIOLOGY & BIOTECHNOLOGY

 AB 07

THIRD SEMESTER – NOV 2006

# ST 3201 – BIOSTATISTICS

Date & Time : 31-10-2006/9.00-12.00   Dept. No.                                                       Max. : 100 Marks

SECTION A

1. What is a histogram? Mention its use.
2. Comment on the following statement: “Arithmetic mean is always the best measure of central tendency”.
3. Give the various measures of dispersion.
4. What is the probability of getting the sum as 5 when two dice are thrown?
5. The distribution function of a random variable ‘X’ is as follows:

X:        -1         0          1

P[X=x]:       ¼         ½         ¼ .  Find E(X+2).

1. Give any two properties of normal distribution.
2. Define ‘Statistic’. Give an example for the same.
3. From a random sample of 50 observations the mean and variance are found to be 10.1 and 2.3 respectively. Based on the above information can it be concluded that the population mean is 9 ? Test at 5% level.
4. Mention any one use of F – distribution.
5. Show that for a standardized random variable, the mean and variance are zero and one respectively.

SECTION B

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

Marks: 10-19   20-29   30-39   40-49   50-59   60-69   70-79

No. of students:   8         19        29        36        25        13         4

1. The Serum – cholesterol levels (mg/dL) of 10 patients are given below:                                                                                 195,145,205,159,244,166,250,236,192,224. Draw a box – plot for the above data and interpret it.
2. A problem in statistics is given to 3 students P, Q and R whose chances of solving it are 1/3,1/4 and 2/5 respectively. What is the probability that ) exactly one will solve the problem b.) no one will solve the problem?
3. If the height of 300 students is normally distributed with mean 68 inches and standard deviation 2.5 inches, how many students have height: ) greater than 72 inches           b.) less than 60 inches                                      c.) between 65 and 71 inches.
4. Consider a population with N=6 units, the values being 12,14,10,14,15,12. Select all possible samples of size 2 and verify whether the sample mean is an unbiased estimator for the population mean.
5. What are ‘large sample tests’? Explain any one test procedure based on large samples.
6. 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 at 5% level.

1. Explain the procedure for testing a specified value of Population median.

SECTION C

1. a.) Find mean deviation about mean and median and their coefficients

from the following data:

X: 10         17         20           24              14

f:  5           12        18           12               3

b.) Assume that a factory has two machines. Past records show that

machine 1 produces 30% of the items of the output and machine 2

produces 70% of the items. Further 5% 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)

1. a.) If 20% of the bolts produced by a machine are defective, determine

the probability that out of 4 bolts chosen at random i.) one  ii.) none

will be defective.

b.) A typist in a company commits the following number of mistakes per

page in typing 432 pages:

Mistakes per page:      0       1        2        3        4

No. of pages:     223    142     48     15       4

Fit a Poisson distribution to the above data and test the goodness of fit

at 5% level.

c.) Define the following terms:

i.) random experiment   ii.) sample space   iii.) event.         (4+12+4)

1. a.) In a random sample of 800 people from city A, 220 were found

having typhoid while in a random sample of 600 people from

city B 145 were having typhoid. Test at 5% level whether the

proportion of people suffering from typhoid in the two cities are

equal.

b.) Below are given the gains in weights(lb.) of lions fed on two diets

X and Y respectively:

Diet X: 25       32        30        32        24        14        32

Diet Y:            24        34        22        30        42        31        40        30                                32        35

Test, at 5% level, whether the mean gain in weight between the two

diets is significant.                                                                    (8+12)

22 a.) Let M be the median lung capacity in liters for males. Use the

Wilcoxon statistic with the following 17 observations to test, at 5%

level, the null hypothesis H0: M = 4.7 against a two sided alternative

hypothesis:

4.3     5.0       5.7       6.2       4.8       4.7       5.6       5.2       3.7                     4.0     5.6       6.8       4.9            7.6       5.4       3.8       5.6

b.) Explain the following:

i.) Random Variable

iii.) Percentiles

iv.) Type 1 Error.                                                                     (10+10)

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