LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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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)
- What is a frequency polygon?
- Give the various measures of dispersion.
- Define mutually exclusive events.
- 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).
- Find the mean of the Poisson distribution for which P(X=1) = 2P(X=2).
- Define sampling distribution.
- 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.
- What is a contingency table?
- Show that for a standardized random variable, the mean and variance are zero and one respectively.
- Give an example for one way analysis of variance.
SECTION B
Answer any five questions. (5×8=40)
- 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
- 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.
- 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.
- 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?
- 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
- Explain the procedure for testing the equality of two population proportions.
- 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.
- 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)
- ) 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)
- 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)
- 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)
- 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.
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