STAT 511 STATISTICAL METHODS FOR APPLIED SCIENCES Question Paper

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ICAR-INDIAN AGRICULTURAL STATISTICS RESEARCH INSTITUTE

Course: STAT 511 (STATISTICAL METHODS FOR APPLIED SCIENCES)

PRACTICAL EXAMINATION

TIME: 2.30 hrs                 Full Marks: 100

Please attempt any 5 Questions. (20 marks each).

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1. Find mean median mode for the following Probability distribution:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	12	16	19	17	14	12

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2. Find standard deviation variance coefficient of variation Based on standard deviation for following frequency distribution:

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
Frequency	3	9	23	45	92	48	22	7	3	1

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3. Seven coins are tossed and number of heads noted. The experiment is repeated 128 times and the following distribution is obtained:

No. of heads	0	1	2	3	4	5	6	7	Total
Frequencies	7	6	19	35	30	23	7	1	128

Fit a binomial distribution assuming i) The coin is unbiased and ii) The nature of the coin is not known.

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4. The additional hours of sleep gained after using each one of the two drugs by the same group of 12 patients are given below.

Patient	1	2	3	4	5	6	7	8	9	10	11	12
Drug 1	2.1	0.2	0.9	3.8	3.5	-0.2	-0.7	-0.7	-0.8	1.3	-1.3	-0.3
Drug 2	3.6	4.7	1.8	5.5	4.6	-0.3	2.1	2.1	1.7	2.0	1.9	-0.4

i) The two drugs are significantly different in respect of their efficiency in inducing sleep.

ii) Drug 2 gives more than one-hour sleep as compared to drug 1.

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5. Fit a Poisson distribution to the following data

x	0	1	2	3	4	5	6	7	8
f	56	156	132	92	37	22	4	0	1

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6. A series of 20-coin tosses might produce the following sequence of heads (H) and tails (T).

H H T T H T H H H H T H H T T T T T H H

How many runs are present in the above sequence? Prove the sequence is random or not.

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7. To determine if a new hybrid seeding produces a bushier flowering plant, following data was collected. Examine if the data indicate that new hybrid produces larger shrubs than the current variety?

Shrubs Girth (in inches) - Hybrid (x): 31.8, 32.8, 39.2, 36.0, 30.0, 34.5, 37.4

Shrubs Girth (in inches) - Current variety (y): 35.5, 27.6, 21.3, 24.8, 36.7, 30.0

Perform a median test for testing that the two samples come from the same population or not.

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8. The gain in weight in grams of two random samples of rats fed on two different diets A and B are given below. Examine whether the difference in mean increase in weight is significant.

Diet A: 13, 14, 10, 10, 12, 11, 12, 16, 10, 08, 10, 11

Diet B: 07, 10, 11, 09, 08

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