Veer Narmad South Gujarat University 2011-1st Year B.A SB-0037 Statistics ( Higher ) ( 2 ) - Question Paper

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ENGLISH VERSION

Instructions : (1) As per the instruction no. 1 of page no. 1.

(2)    Answer all six questions.

(3)    Graph papers, logarithmic tables and statistical tables will be supplied on request.

(4)    Figures given to the right indicate the marks of the question.

1 Answer the following questions in short :    14

(1)    If YjP\%⁼ 400 Im⁼⁴⁷⁵> 2>o?0^{=32 and}

=380 then find Laspeyer's and Pasche's index numbers.

(2)    Write down the steps of the test procedure for testing the hypothesis.

(3)    The correlation ceofficient for a sample of 18 pairs is 0.70. Is this value significant ?

(4)    Write the probability function of Poisson distribution for

X = 5-

(5)    Define national income.

(6)    If n_x= 10, X(-)² =360, n₂=9, (x₂-x₂)² = 495

then find the value of F statistic.

(7)    What is level of significance ?

2 (a) State the conditions from which binomial distribution 5 follows Poisson distribution. State the characteristics of Poisson distribution.

(b)    The probability for any student to pass in    5

examination is . If 6 students appear in the

examination, what is the probability that at least 4 students will pass ?

(c)    An average height of 2000 students is 140 cms and standard deviation of the height is 10 cms. If the height is normally distributed, find the number of students whose height is

(i)    less then 125 cms

(ii)    more than 155 cms.

OR

2    (a) State the properties and uses of normal distribution. 5

(b)    From the following information find expected    5

frequences using Poisson distribution. (_e^{_1 04} = 0.353)

x 0 1 2 3 4 / 40 30 20 6 4

(c)    The mean and variance of a Binomial distribution    4 are 6 and 2 respectively, then calculate n, p and q.

Also find the value of P(x > 7).

3    (a) Explain the method of testing the significance of    5

the difference of standard deviations for two large samples of variables.

(b)    A die is tossed 1200 times 5 or 6 appeared for    5 455 times on it. Can we say the die is unbiased ?

(c)    The following are the results of a intelligence    4 test of two random samples of boys and girls :

Boys    Girls

Mean    87    84

Standard deviation 10    12

Number of students 121    81

Is the difference between averages of intelligence quotient significant of the boys and girls ?

Describe the method used by national income committee for estimation of India's national income. State the uses of India's national income.

Explain the importance of selection of a base year and selection of weighting method in construction of index number.

Calculate index number by total expenditure method for the data below :

(c) Explain time reversal test.

OR

What is index number ? State its uses.    5

Obtain Fisher's and Bowley's index numbers from the 5 following information.

The prices of 4 commodities increased in a year by 125%, 150%, 175% and 200% as compared to base year. Their relative importance is in the ratio 4:3:2:1. Calculate the price index number.

(a) Explain the method for testing the significance difference of population mean for small sample.

(b)    A random sample of 6 workers was drawn from    5 industry A and monthly wages of these workers

were Rs. 1230, 1300, 1360, 1380, 1420 and 1440.

Another sample of 10 workers from industry B gave the wages Rs. 1220, 1240, 1300, 1320, 1380, 1380,

1400, 1420, 1440 and 1350. "Industry A pays more wages". Examine the validity of this suggestion.

(c)    Condidates contesting an election expected to receive 4 the votes in the proportion 7:6:5. If they had

obtained 1500, 1150, 950 votes respectively; can you say that it confirms their expectation.

OR

5 (a) Explain the use of F statistic for testing the hypothesis 5 "Variances of two populations are same".

(b) From the data given below, examine whether tendency 5 of voter depends upon residential area or not ?

(c) Explain type I and type II error in testing of    4

hypothesis.

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