Veer Narmad South Gujarat University 2011-2nd Year B.Com Statics -1, ,- , Veer Narmad South University - Question Paper
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University: Veer Narmad South Gujarat University
Program Name :Second Year B.Com
Course Name: SB:0410 - Statics Paper-1, 2nd Year B.Com, March-2011, Veer Narmad South Gujarat University.
examination Month and Year: March-2011.
Duration : three hours
Maximum marks:- 70
Attachment :- PDF file containing SB:0410 - Statics Paper-1, March-2011.
Second Year B. Com. Examination March/April - 2011 Statistics : Paper - I
Time : 3 Hours] [Total Marks : 70
00
Seat No.:
M CnsLLnlcj.L{l [qoicu u? snqw <h>h41.
Fillup strictly the details of signs on your answer book.
Name of the Examination :
S. Y. B. Com.
Name of the Subject:
Statistics : Paper - 1
Student's Signature
|
-Subject Code No. |
|
-Section No. (1,2,.....): Nil |
(3) WM, faddl Vil*(l *IL'HCILHL *Ul$L
(*l) *mf dl [100 10 0] HIS % />1 = 0.02 61H dl lliR-ti. &d Vflrd WHWdl
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|
<&H dl (3x + 4j) ?Hd V(9x + 3y) *11*11. | |||||||||
|
(m) 2 *L.hI. UHlfeld [cW.eK<Ull him C-tRc-t n ifcdl
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U) x %L<HI<141 PUWSI 413. & : *
|
X |
-1 |
0 |
1 |
2 |
3 |
4 |
|
P(x) |
0.04 |
0.16 |
3 P |
0.29 |
P |
0.07 |
Y (*l) (i) -{Rdi HL %LH*4a<Cl : 3
(3cHL. W4H 5Hd 3ll6i W4H.
(ii) <dil[dk *msHl [Af, //,, C|, //2, c2] dl L<H<s;[ct %LH*4a<Cl. * (<h) *k& kk *mfdL [2000, n, 2] 6RL 2% HIH HHLSL H3.iq.dl L-ft *i<HL=LdL 0.10 d. d*U ATI = 290 d dL ?HL
Hit'll HL8 00 RL d*U H**ft llMTl .
Y (*l) feHL6l%SL (O.C.eii) d*U 5HLS?l &HL6l%SL %LH*4a<Cl. H
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L?HL HIS ASW *id ATI *LLH"l.
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U)
<H [HfcrftdL HHL'SLL dL d$L=Ld %U*UdL H&SL'SL %LH*4a<Cl. Y %uUhI 1000 *L?HLH'L(l 800 HLHL&L $Vtdl (3HHLL & Y <W.l\ 1200 te*WLHL*ft 1080 HLHL&L $Vkl (3HHLL
d. dL ?HH *LLH *L?HL ?Hd HLHL&L
$LddL <WiL*L LHLd d ? 5% -ft %UUdL-ft LdL (3HHLL S$L. ilL*dl Wdi <H *L\6LdL *L**L*L HIS d*U 1WU3. dlL JlHLSl d. Y dL dHL*LL (3rHL?.dHL H&LdL d$L=Ld %LU d i H? 5% %LUdL-ft SSLLdL (3HHLL :
|
90-1121 %i Cs |
100-112-11 %i Cs | |
|
%l'==l?l (3rmH | ||
|
Utri -112 |
1600 k.g. |
1575 k.g. |
|
U. Pi. Ulrl -112 |
30 k.g. |
25 k.g. |
H (*l) dlAd'l HU %LH*4a<Cl : Y
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|
e (an) Mzk % ? ssm te$-fl vki hiMI hr|sll:hl wwl. x Sh= |
15-19 |
20-24 |
25-29 |
30-34 |
35-39 |
40-44 |
45-49 |
|
HW = (0. (ftvHl) |
10 |
90 |
100 |
120 |
80 |
30 |
20 |
|
fclrt ?A |
0.90 |
0.92 |
0.95 |
0.88 |
0.86 |
0.80 |
0.75 |
($) <H %l&?l-fl -flat aHLHSfl Hlfecft U**(l UHlfeld .*1 IlMTl aHd Y *16* aHRLHH.HL'i d d WWl :
|
(3H* |
?uk A |
?uk B |
United cirCl | ||
|
(<&KHi) | |||||
|
0-5 |
10 |
30 |
8 |
20 |
5 |
|
5-20 |
35 |
20 |
42 |
25 |
40 |
|
20-40 |
30 |
10 |
25 |
15 |
25 |
|
40-70 |
20 |
25 |
20 |
20 |
20 |
|
>70 |
5 |
40 |
10 |
30 |
10 |
a**l<U
e (an) anUiL anaei ? HKlSsm anUiL Y
Hmi-fl &fl WZMi dlL aniiril-fl. (3HHll>LdL
VSllcfl.
(<h) -ftatdi ?sm LlSLd:l <*idl4l fre-t<Utt DsHdi IlMTl : Y
|
(3H* |
lx |
dx |
Px |
<lx |
Lx |
T x |
e* |
|
40 |
82000 |
100 |
? |
? |
? |
4042200 |
? |
|
41 |
? |
80 |
? |
? |
81860 |
? |
? |
(b) -flat 5HLH<sfl Hlfecft HVft CBR, GFR, TFR dlL GRR #fl. X UiU-fl |<H qCl 3.75 C-ILH d. dH'tf |<H 1000 'tf-HC-ti <HLali'LHL mi*L?HL-{l %LU 550 d.
|
(3*R |
15-19 |
20-24 |
25-29 |
30-34 |
35-39 |
40-44 |
45-49 |
|
48 |
45 |
42 |
39 |
36 |
33 |
27 | |
|
1200 |
5130 |
6300 |
4290 |
2880 |
900 |
108 |
Instructions : (1) As per the Instruction No. 1 of Page No. 1.
(2) The figures to the right indicate full marks of the question.
(3) Statistical tables and graph papers would be supplied on request.
1 Answer the following questions : 10
(i) For the plan [100 10 0] if P'= 0.02 then obtain the
probability of acceptance by hypergeometric distribution.
(ii) The crude birth rate of a city is 40 and the ratio of the number of women in child bearing age to the total population is 0.4 then obtain the general fertility rate of that city.
(iii) For the two independent variables jt and y if
E(x) = 9,E(y) = 3,V(x) = 5,V(y) = \ then obtain E(3x + 4y) and V(9x + 3y).
|
' 0 4 |
3 ' | ||
|
(iv) If A~ |
1 -3 |
-3 |
then prove that |
|
-1 4 |
4 |
(v) A sample of size n has been drawn from a large population with S.D. 2. The sample mean is 9.10 c.m. If the 95.45% confidence limits of the population mean are 8.70 to 9.50 c.m. then obtain the sample size n.
(a) Define a matrix. State the difference between matrix and determinant.
(b) Solve the following equations by using inverse of a matrix : x + y + z = 3, 2x + _y + z = 4, x + 2y + 3z = 6
(c) In a family x, there are 2 men, 3 women and 4 children.In another family y, there are 1 man, 1 woman and 2 children. The daily requirements for, a man, a woman and a child, are respectively 2400, 2000 and 1500 calories and the requirement of protein are respectively 50 grams, 40 grams and 30 grams. Obtain the total requirements of calories and proteins in each family by using matrix.
(a) Explain the following matrices with illustrations : Skew symmetric matrix, Diagonal matrix, Unit matrix or Indentity matrix, Square matrix.
(b) A person buys 4 mangoes, 6 chikoo, 8 apples in
Rs. 86. Another person buys 2 mangoes, 8 chikoo and
4 apples in Rs. 68. And a third person buys 10 mangoes,
4 chikoo and 6 apples in Rs. 132. Obtain the price of each fruit using a inverse of a matrix.
then obtain the value of a2-a+i
1 2 2 1 2 2 2 1 1
(c) If A
(a) Define discrete random variable. What is probability distribution ? State its properties.
(b) Obtain the moments about mean for the observations 1, 3, 5, 7 and 9. Also state the shape of the curve.
(c) A person throws an unbiased die and he gets the amount in rupees equal to the cube of the face value obtained. Obtain the mathematical expectation of his amount.
OR
(a) Obtain |i| for the Poisson distribution by using the
basic definition of moments.
(b) The first four moments about the point 5 of 7 observations are respectively 2, 20, 40 and 50. Then obtain first three moments about origin.
(c) The probability distribution of a random variable x is given by.
|
X |
-1 |
0 |
1 |
2 |
3 |
4 |
|
P(x) |
0.04 |
0.16 |
3 P |
0.29 |
P |
0.07 |
obtain the constant p. Also find E(9x + 9) and F(5x-5).
4 (a) (i) Explain the following terms : 3
Producer's risk and consumer's risk.
(ii) Explain the working process of the double 2
sampling plan [N, nx, q, n2, c2 ].
(b) The probability of rejecting a lot with 2%, fraction 7
defective by the plan [2000, n, 2] is 0.10, and ATI=290,
then draw AOQ curve for this plan. Also obtain AOQL from the curve.
OR
4 (a) Explain operating characteristic curve [o.c. curve] and 5 ideal o.c. curve.
(b) For the double sampling plan [2000,50,1,100,3] with P' = 20%, obtain ASN and ATI.
Explain the method of testing the significance of the difference between two proportions of two large samples. In a city out of 1000 boys, 800 boys are using mobile phone while out of 1200 girls, 1080 girls are using mobile phone. Can we say that boys and girls both are equally using mobile phone. Use 5% level of significance.
(a)
(b)
(c)
The average yield and S.D. in two plots of rice are given below. Is the difference between the variability in the yield significant ? Use 5% level of significance:
|
Group of |
Group of | |
|
90 plots |
100 plots | |
|
Average yield | ||
|
per plot |
1600 k.g. |
1575 k.g. |
|
S.D. per plot |
30 k.g. |
25 k.g. |
OR
Explain the following terms : 4
(a)
(b)
two types of error in testing of hypothesis, standard error.
The manufacturer of "saree" claims that 92% sarees 4 are of good quality in his total production of sarees.
A sample of 500 sarees is taken from the total production for the inspection. It is found that there are 50 defective sarees. With the help of this information test manufacturer's claim at 5% level of significance.
The average height of 1000 Austrelians is 67" and 4 S.D. = 2.50", while the average height of 2000 Americans is 68.5" and S.D. = 2.6". Can we say that the Americans are taller than Austrehans ? Use 5% level of significance.
(c)
(a)
(b)
What is infant mortality Rate ? State the assumptions 4 in constructing life table.
6
Obtain GRR and NRR from the following data : 4
|
Age |
15-19 |
20-24 |
25-29 |
30-34 |
35-39 |
40-44 |
45-49 |
|
Fertility Rate (Female births) |
10 |
90 |
100 |
120 |
80 |
30 |
20 |
|
Survival Rate |
0.90 |
0.92 |
0.95 |
0.88 |
0.86 |
0.80 |
0.75 |
(c) Obtain the standard death rate for the following data 4 of two cities. Which city is more healthy ?
|
Age |
City A |
City B |
Standard population (in thousand) | ||
|
Population (in thousand) |
Death Rate |
Population (in thousand) |
Death Rate | ||
|
0-5 |
10 |
30 |
8 |
20 |
5 |
|
5-20 |
35 |
20 |
42 |
25 |
40 |
|
20-40 |
30 |
10 |
25 |
15 |
25 |
|
40-70 |
20 |
25 |
20 |
20 |
20 |
|
>70 |
5 |
40 |
10 |
30 |
10 |
OR
What is vital statistics ? State the methods of 4
6 (a) (b)
(c)
collecting vital statistics. State the uses of vital statistics.
Obtain the values of those terms having question 4 mark for the following life table :
|
Age |
h |
dx |
Px |
<lx |
Lx |
T x |
ex |
|
40 |
82000 |
100 |
? |
? |
? |
4042200 |
? |
|
41 |
? |
80 |
? |
? |
81860 |
? |
? |
Calculate CBR, GFR, TFR and GRR for the following 4 information. Total population of a city is 3.75 lakhs, and there are 550 male babies in total children born 1000 :
|
Age |
15-19 |
20-24 |
25-29 |
30-34 |
35-39 |
40-44 |
45-49 |
|
No. of women (in thousand) |
48 |
45 |
42 |
39 |
36 |
33 |
27 |
|
No. of children bom |
1200 |
5130 |
6300 |
4290 |
2880 |
900 |
108 |
SB-0410] 8 [7000]
Rli P tftfl dH'tf (9x + 9) *14 V(5x-5) mil.
SB-0410] 2 [Contd..
|
Attachment: |
| Earning: Approval pending. |
