Class
2nd YEAR Federal Board 2009
Paper:Statistics (Objective Type) Time
Allowed: Max.Marks:
Note:Use this paper
to write the answers to the objective questions.No marks will be awarded
for cutting,over-writing
or using a pencil.This paper must be tagged with the answer-book.
1. Insert
correct option.
(1) A coin is tossed 3 times, then the
number of sample points in the sample space is:
(a) 2 3 (b)
8
(c) c (d)
Both A and C
(2) The probability of drawing a black
card from a well-shuffled pack of 52 cards is:
(3) For two independent variables Var(x)
= 14 and Var(y) = 5 then Var(x - y) is equal to:
(a) 9 (b)
19
(c) 70 (d)
2.8
(4) The area of trapezoid is equal to.
(a) Sum of parallel
sides x base (b)
1/2 [sum of parallel sides x base]
(c) 2 x base
x sum of parallel sides (d)
1/4 [sum of parallel sides x base]
(5) Binomial distribution has the range.
(a) 0,1,2,.....n
(b)
0,1,2,.....+oo
(c) -oo
to + oo (d)
-oo to + 0
(6) Which of the following case is true
for hypergeometric distribution?
(a) Probability
remains constant for all the trails. (b)
Probability changes
(c) Successive
trials are dependent. (d)
Both B and C.
(7) The points of inflection in normal
distribution are.
(8) In a normal distribution 0 = 10 then
mean deviation will be approximately:
(a) 8 (b)
Zero
(c) 10 (d)
4
(9) The total number of possible samples
in sampling without replacement is.
(10) Statistical inference is divided into two major
branches given below.
(a) Point
estimation and testing of hypothesis
(b) Interval
estimation and testing of hypothesis
(c) Testing
of hypothesis and estimation
(d) Point
estimation and interval estimation.
(11) The critical region is divided keeping
in view the.
(a) Null
hypothesis (b)
Alternate hypothesis
(c) Level
of significance (d) Test
statistic
(12) If the alternative hypothesis is of the
form H1:0 0, then the test will be.
(a) Two
sided (b)
Right sided
(c) Left
sided (d)
None
(13) Degrees of freedom for testing two independent
random small sample of size n1 and n2 is .
(a) n1
- 1 (b)
n2 - 1
(c)
n1 + n2 - 1 (d)
(n1 - 1) + (n2 + 1)
(14) The calculated value of Chi-square could
not be
(a) Positive
(b)
Zero
(c) Negative
(d)
One
(15) Which of the following device does not
use magnetic media for storing the data?
(a) CD
Rom drive (b)
Floppy disk drive
(c) Hard
disk (d)
None of these
(16) Which of the following os NOT the example
of attribute?
(a) Liking
or disliking (b)
Religion
(c) Beauty
(d)
Weight
(17) Which of the following error can be decreased
by increasing the sample size?
(a) Sampling
error (b)
Non sampling error
(c) Bias
(d)
Standard error
2. Attempt any FOURTEEN
parts.
(1) Two six faced dice are rolled.
Write down the sample space. Also find the probability of
getting 5 as
sum.
(2) Write a set 'A' bcontainig
all vowels in the word ''PUBLICATION'', and then find the probability
of
'A'.Usiing the P(A). Find probability of consonants.
(3) The probability distribution
of a random variable 'X' is giben.
Rewrite the probability distribution after finding out the value
of K.Also cal;culate the mean value and
variance of X.
(4) Write down at least three
laws of expectations for independent varibles.
(5) If a random variable
has a binomial Distribution (x3) (1/3)3-x (2/3)x. Where x = 0, 1,
2, 3. Rewrite
it in a tabular form, calculate mean and variance and verify these
using formula.
(6) Find the approximate
value of standard deviation in both the cases.
(a) If quartile deviation of normal Distribution is 6.7450.
(b) If mean deviation of a Normal Distribution is 8.
(7) Write down six properties
of normal Distribution.
(8) A committee of size 3
is selected from 4 men and 2 women. Find the probability distribution
by hypergeometric
experiment for the men on the committee. Also find mean of the distribution
and verify by using formula.
(9) Name the four techniques
used in probability sampling and two techniques of non-Probability
sampling.
(10) Write down the relation of the following
with population parameters, if the sampling is without replacement.(ux,
ux1-x2, o-2x o-2x1-x2)
(11) What type of the hypothesis and
its critical region.
(12) Briefly explain the following rerms.
(a) Confidence interval.
(b) Confidence limits.
(c) Confidence co-efficient.
(13) If n1 = 90, n2 = 100,
x1 = 76.4, x2 = 81.2 s1 = 8.2,
s2 = 7.6 find 98% confidence limits for
u1 - u2.
(14) Write down the six steps involved
in testing of hypothesis.
(15) Give n1 = 10, n2 = 12,
x1 = 12, x2 = 15, (x1
- x1)2 = 120 and (x2 - x2)2 = 314.Find the
value of pooied t:
(16) What are the degrees of freedom
in the fo;;owinmg tests 'Pooled t', if samples sizes are n1 and
n2.''Pairedt'',
if sample sizes are n1 and n2. x2 if rxc contingency
table is given.
(17) Represent the following data in
a tabular form.
Total population = 900
Literate people = 300
Employed people = 750
Literate and employed = 160
What will be the number of illiterate and employed people.
(18) Select all possible samples of two
member from the given population
(a) With replacement. (b) Without
replacement.
Member 1 2 3 4 5
Marital
Status M S M S S
(M = Married and S = single)
(19) Differentiate between.
(a) RAM and ROM.
(b) Low level language and high level language.
Attempt any TWO questions.
3.a) The probability distribution
of random variable 'X' is given in the table below.
X 1 2 3 4 5
P(X) 0.1 0.3 k 0.2 0.1
Find. The value of K, P(x<3),
P(X<1),
The probability distribution of Y = 3 X + 5 Mean and variance of
Y.
b) A aptitude
test consists of 10 MCQ's with four options. If a student mark the
independently,then find
the probability of.
(i) Being
correct only to questions 1st, 3rd, 6th and 9th.
(ii) Being
correct to 4 questions.
4.a) Find the probability
of getting between 3 and 6 heads in 10 tosses of a fair coin, using
normal approximation
to the binomal distribution.
b) The weight
of 1000 students are normally distributed with mean 68.5 kg and
S.D.2.7 kg. If 2oo random
samples of size 25 students each are drawn from this population,
then find the expected
mean
and standard deviation of the sampling distribution of means, if
the sampling is:
(i) With replacement. (ii) Without replacement
.
c) A sample
of 12 measurements of the breaking strength of cotton thread gave
a mean x = 209 grams
and a standard deviation s= 35 grams. Find 95% confidence limits
of actual mean breaking
strength.
5.a) The following data give
paired yield of two varieties of wheet.
Test the hypothesis that the mean yields are equal at 5% level of
significance.
b) In the
following table the number of employees and condition of factory
are shown:
Discuss the association between the condition of premises and the
number of employees.
|
