DU SOL Question Paper 2018 BA Basic Statistics

This question paper conrains 4 printed pages +l page Table Attachedl

Your Roll No.

4314
' (Prog.)/ttl
B.A. ctl
Paper Code : C-804

APPLICATION COURSE : BASIC STATISTICS

Time : 3 Hours Maximum Marks : 100
(Write y6177 Roll No. on the top inmediately on receipt of
this question paper.)

auestion No. I is compulsory.
Attempt any four questions from

Question No. 2 to 7, selecting at least one

question from each of the Sections I. II and III.

Give full explanation for each question.

Marks are indicated against each question.

Use of Simple Calculator is allowed.

l. Short answers with proper justification are expected in ail the
five parts of this question. Each part is of 3 marks : 5x4:20
(r) Discuss the skewness for the distribution in which :

mean<median<mode.
(ii) Find two regression equations from the followine data :

XY
Mean 3 g5

Standard deviation ll g

Correlation coefficient 0.6
P.T.O.

(2) 4314

(ril) A union wage negotiator feels that the probabilities
are 0.40, 0.30, 0.20 and 0'10 that the union members
will get Rs. 1.50, Rs. 1.00, Rs. 0.50 or no raise per hour.
What is the exPected raise ?

(rv) If the correlation'coefficient between two random
variables X and Y is zero, then what can you say about

the independence of random variables ?

(v) In a random sample, 136 of400 persons given a flu vaccine

experienced some discomfort. Construct a95o/o confidence

interval for the true proportion of persons who will
experience some discomfort from the vaccine.

Section I

2. Calculate the correlation coefficient for the following heights

in inches of father, X and their sons, Y : n
X

6) 67

6 68

67 65

61 68

68 n
a n
7A @

n 7l

(3) 4314

and after the
You are given the position in a factory before
settlement of industrial dispute
' n
Before clisPute After disPute

No' of workers 3ooo nm

Mean Wages (Rs.) D0 230

Median Wages (Rs.) 250 244

'26
Standard deviation' 30
dispute in respect
Compare the position before and after the
of:
(l) VariabilitY

(ii) Skewness

(rii) Modal wages.
Section lI

follow the normal
The marks obtained in a certain examination
10' If 1000
distribution with mean 45 and standard deviation
students appeared at examination' calculate
the number of

students scoring ,
T

(,) less than 40 marks

(ti) more than 60 marks

(iii) between 40 and 50 marks'
Records show that 30o/o of all patient9 admitted
to a medical
for-
clinic fail to pay their dues and eventually their bills are
from
given. Suppose four patients represent a random selection
P.T.O.

(4) $14
the large set of prospective patients served by the clinic.
Find
the probabiliry rhat ;

(, all patient's bills wilt evenrually be forgiven
(ii) at least one patient bill will be forgiven. n
Section lll

The mean life time of sample of 100 fluorescent light tubes
produced by a company is computed to be 1570 hours
with
a standard deviation of 120 hours. The company claims that
the average life of the tubes produced by the company is
1600 hours. Using the level of significance of 0.05. is
the
claim .acceptable ?
n
(Given that : Zoor: x| .96, Zoot = *2.5g, Zuor: 1.65,
Zo ot : 2.33)
7. The following are the numbers which a random sample of nine
salesmen of industrial chemicals in a city and a random
sample
of six salesmen of industrial chemicals in another city made over
a fixed period of time :

ciry I : 41,47,62,39, 56,64,37,61, 52
city 2 : 34, 63,45, 55, 24. 43

Use the 0.01 level of significance to test whether the difference
between the means of these two samples is significant. 20

: 2.602, toor.
r: : 2.650,
(Given : to.or. r+ = 2.624, /oor,
rs
rooos, 13 : 3.012)

4314
1,500

q3L q

Thrs tablc prrscnli lhc rrca bctl','een thc nlEin snd the Z scorc . \Vhen Z=l'96, the rhsdcd
lrca rs 0.4?50

Arers l-lnde r tht Stnndrrd Normat Curve
0.00 0.01 0.0r 0.03 0.04 0.05 0.06 0.f7 0.08

0.0 0.0000 0.0040 0.0080 0.0t?0 0.0160 0.0199 0.0239 0.02?9 0.0319 0.0359
0r .0398 .s138 04?8 0t ? .9511 .0596 .0636 .067 t .0? t4 .0753
I

0.t 0;93 .0811 .0871 .0410 0948 .0981 .t426 r064 il01 .u4t . .

0.1 | 179 tatl l)({ r:91 | 3lt 136ll .1406 .1443 .r{80 .t511
, .

0.rl t 55.r 19 1 .16?8 .16&l .1700 .17]6 .l'trl .lEB8 .1t44 .lE?9
, .1

0.J .19t5 l9r0 r98t .10r9 1054 .l0gg :?,l?J .2t57 .2190 2271
. ,
n( t1(7 .1i9t 112{ .]]5? :189 24j"/* .24t4 .3486 .2517 2W
0.7 ,:580 .:6r r t6"r2 :67t .:704 .21]/ .l?64 ,t79{ .2823 .7852
nQ lqtl .:910 19l9 :96? .:995 .1023 .105 I .10?E .J 106 ..1133
0,9 I r59 Jr$6 l2ll .i?ts J?6{ .J289 .J3lJ l].ro .l]6J .1389
0 j{ll ,i{18 J46r l48t lJ08 .l5ll .lJ5{ .J'n .J599 .1621
I i6.1i .i665 l6E6 .l?09 .)729 ,17.t9 ,)7',70 J790 .18t0 .1810
2 3949 .]869 .188E .]907 .19?J .19{4 .1962 .i980 .3997 .401J
{03r .{s.r9 1066 .{081 ..r0+9 .4 il t .{lll it47 ."162 lln
.t t91 ..1?0? 4?l: .{216 .42J1 .4263 .4279 .{?9? ,4106 .4319

I
( 1131 'tl.t' ."tlJ7 .{3?0 ,43t2 ..il9{ .4406 "Sil8 14n .{4{l
.o .lJJ? .{461 44x .,{"r8{ .{49J 450J .d5 | J ..r52J ..r5lt .15{J
.lJJ,t .45fi ..lt?1 .{J82 .4t91 .{J99 .{608 .4616 .462J .4613
.8 .16r I 16^19 46J6 .{6,4 .{67| {6?t .4686 1691 .4699 .4?0d
^r;tl ..r?19 ,1?:6 "{? j: -lt ..1744 .{T j0 ..t? j6
..rt ,4761 .4161
.47?l .{?78 .'r?81 .4788 .4?91 .4798 .d80i .{t0€ .{$2 .481?
1l .182 t .4826 .1830 .48r .48]8 .4E4? .4846 .{tJO .4{54 .1857
t1 4861 ".186.r ,.r86E .48?t .4t?J .48?S .{881 .{88"r .488? .4890
,.tE9l ..{896 .4899 490t .{9$4 .{906 .4909 ,49t I .4913 .4916
.19 t8 .4920 .{92: .491.5 .{927 .4929 ..91t .4932 .{9lr .49]6
;.) d9l8 .49d0 .d9ill .r%3 .4945 .4946 .4948 .{949 .495t .s951
:.6 .1951 '19Jt 4955 {9J7 .4959 .{960 .{961 .4962 .4%l .{964
)t .1965 ..1966 .,196? {968 .{%9 .4970 .{9?l .4917 '.491t .49?4
4qir d97, .{9?6 .4917 .197? .{978 !9n .49?9 .4980 .4981
.1981 .d981 ..1982 {981 .498{ .d984 .{985 .4985 .498d .{9E6
lo {t87 '1987 .{987 .,l9Eg .{988 .d989 .4989 .4989 .49'0 .4990
3.r .1990 .{991 ,1991 ..t991 {99! .{9t2 .4992 .4992 .{993 .4991
r99l ..1991 .49?.r .4994 .4994 .4994 .499{ .499t .4995 -4W5
J.) dg), d995 ..1995 .d996 .49t6 .4996 .4996 .4996 .4996 .49g1
I.,r ,1997 .1997 499? .{997 .499? .4997 .1991 .499? .4997 .499t
1.6 "t99E .r99E ..r99 .4999 .4994 .4y99 .4999 .4999 .499t ..999
].9 "5000