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STA301 Finalterm Papers…7 Papers Solved..By Arman Makhani

Statistic and ProbabilitySTA301 7Final term paper

Paper 1

Question No: 1 ( Marks: 1 ) - Please choose oneMean deviation is always:

► Less than S.D► Greater than S.D► Greater or equal to S.D► Less or equal to S.D

Question No: 2 ( Marks: 1 ) - Please choose one The value of χ2can never be :

► Zero► Less than 1► Greater than 1► Negative

Question No: 3 ( Marks: 1 ) - Please choose oneThe mean of the F-distribution is:

►

22 1

1

1

forvv

v

►

22 2

2

2

forvv

v

pg 317

►

22 1

1

1

forvv

v


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►

22 1

2

2

forvv

v

Question No: 4 ( Marks: 1 ) - Please choose one

If X and Y are random variables, then E X Y

is equal to:

► ) (E X E Y

► ) (E X E Y

► X E Y

► E X Y

Question No: 5 ( Marks: 1 ) - Please choose oneEvaluate: (9-4)!

► 362880► 120► 24► 6

Question No: 6 ( Marks: 1 ) - Please choose oneWhich formula represents the probability of the complement of event A:

► 1 + P (A)► 1 - P (A)► P (A)► P (A) -1

Question No: 7 ( Marks: 1 ) - Please choose oneIdeally the width of confidence interval should be:

► 0► 1► 99► 100

http://books.google.com.pk/books?id=STziu0wsSL8C&pg=PA333&lpg=PA333&dq=100+confidence+interval+level+is+possible%3F&source=bl&ots=dDfXpkvYOL&sig=jhdy


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T89Aa3LFbIiImUM8h6VhL3s&hl=en&ei=r1JfTeyaLsLyrQf4tqynAg&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEcQ6AEwBw#v=onepage&q=100%20confidence%20interval%20level%20is%20possible%3F&f=falseQuestion No: 8 ( Marks: 1 ) - Please choose one

If the sampling distribution of X is normal, the interval3x x

includes:

► 99% of the sample means

► 99.73% of the sample means pg 233



Question No: 9 ( Marks: 1 ) - Please choose oneThe probability distribution of a statistic is called the:

► Population distribution

► Frequency distribution ► Sampling distribution pg 242

► Sample distribution


An estimator T is said to be unbiased estimator of if

► E (T) =pg 263

► E (T) =T

► E (T) =0

► E (T) =1

Question No: 11 ( Marks: 1 ) - Please choose oneIf the following is a probability distribution, then what is the value of 'a':


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X 1 2 3

P(X) 0.1 a 0.1

► 0.6► 0.8 pg 171► 0.2► 0.4

Sum of p(X) =1 alwaysQuestion No: 12 ( Marks: 1 ) - Please choose oneA discrete probability function f(x) is always:

► Non-negative► Negative► One pg 177► Zero

Question No: 13 ( Marks: 1 ) - Please choose oneAn expected value of a random variable is equal to:

► Variance► Mean pg 182► Standard deviation► Covariance


The |1f x

__________:

1,1f

► ,1f x


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►

,11

f xh

►

,1f xh x

Question No: 15 ( Marks: 1 ) - Please choose oneThe area under a normal curve between 0 and -1.75 is

► .0401

► .5500

► .4599 pg 34 z table► .9599

Question No: 16 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:

► The sample size is at least 5► Both nP and n (1-P) are at least 30

► A continuous distribution is used to approximate a discrete distribution pg 240► The standard normal distribution is applied

Question No: 17 ( Marks: 1 ) - Please choose oneWhich of the following is impossible in sampling:

► Destructive tests not sure► Heterogeneous► To make voters list► None of these

Question No: 18 ( Marks: 1 ) - Please choose oneWhich of the following is a systematic arrangement of data into rows and columns?

► Classification► Tabulation► Bar chart


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► Component bar charthe process of arranging data into rows and columns is called tabulation

Question No: 19 ( Marks: 1 ) - Please choose oneWhich one of the following statements is true regarding a sample?

► It is a part of population► It must contain at least five observations► It refers to descriptive statistics► It produces True value

Question No: 20 ( Marks: 1 ) - Please choose oneThe data for an ogive is found in which distribution?

► A relative frequency distribution► A frequency distribution► A joint frequency distribution► A cumulative frequency distribution

Question No: 21 ( Marks: 1 )Write down the formula for binomial distribution.

Ans:

Question No: 22 ( Marks: 2 )Write down the formula for testing the equality of two population proportions.

Question No: 23 ( Marks: 3 )Define moment ratios. In which unit they are expressed?

Question No: 24 ( Marks: 3 )Elaborate the Poisson distribution:

Question No: 25 ( Marks: 3 )Explain the symmetrical form of the Normal distribution.

Question No: 26 ( Marks: 3 )Elaborate the Least Significant Difference (LSD) Test.


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Question No: 27 ( Marks: 5 )The experiment of a house-agent indicates that he can provide suitable accommodation

for 75 percent of the client who come to him. If on a particular occasion, 6 clientapproaches to him independently, calculate the probability that less than 4 clients will geta satisfactory accommodation.

Question No: 28 ( Marks: 5 )Why we use confidence interval?

Question No: 29 ( Marks: 5 )Write down short note on chi- square test of independence.

Question No: 30 ( Marks: 10 )Draw all possible sample of two letters each without replacement from the letters of the

word “STATISTICS”. Find proportion of latter “S” in each sample.

Question No: 31 ( Marks: 10 )A random variable X has the following probability distribution:

X P(X)-2 0.1-1 k0 0.21 2k2 0.33 3k

Find K and P(X<2).

Paper 2



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When each outcome of a sample space has equal chance to occur as any other, theoutcomes are called:

► Mutually exclusive► Equally likely► Not mutually exclusive► Exhaustive


►

22 1

1

1

forvv

v

►

22 2

2

2

forvv

v

►

22 1

1

1

forvv

v

►

22 1

2

2

forvv

v

Question No: 3 ( Marks: 1 ) - Please choose oneThe LSD test is applied only if the null hypothesis is:

► Rejected pg 336► Accepted► No conclusion► Acknowledged

Question No: 4 ( Marks: 1 ) - Please choose oneAnalysis of variance is a procedure that enables us to test the equality of several:

► Variances► Means► Proportions► Groups

Ref:Equality of two populatiy means


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Question No: 5 ( Marks: 1 ) - Please choose oneANOVA was introduced by :

► Helmert► Pearson► R.A Fisher► Francis

Question No: 6 ( Marks: 1 ) - Please choose oneFor testing of hypothesis about population proportion , we use:

► Z-test► t-Test► Both Z & T-test► F test

Question No: 7 ( Marks: 1 ) - Please choose oneIf a random variable X denotes the number of heads when three distinct coins are tossed,

the X assumed the values:

► 0,1,2,3► 1,3,3,1► 1, 2, 3► 3, 2

Question No: 8 ( Marks: 1 ) - Please choose oneIf X and Y are independent variables, then E (XY) is:

► E(XX)► E(X).E(Y)► X.E(Y)► Y.E(X)

Question No: 9 ( Marks: 1 ) - Please choose oneThe parameters of the binomial distribution b(x; n, p) are:

► x & n► x & p► n & p► x, n & p


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Question No: 10 ( Marks: 1 ) - Please choose oneIf P (E) is the probability that an event will occur, which of the following must be false:

► P(E)= - 1► P(E)=1► P(E)=1/2► P(E)=1/3



► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1


The best unbiased estimator for population variance2

is:

► Sample mean

► Sample median

► Sample proportion

► Sample variance


The sample variance

22 ( )x xS

n

is:

► Unbiased estimator of2

► Biased estimator of 2


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► Unbiased estimator of

► None of these

Question No: 14 ( Marks: 1 ) - Please choose oneWhen c is a constant, then E(c) is:

► 0► 1► c► -c

Question No: 15 ( Marks: 1 ) - Please choose oneThe analysis of variance technique is a method for :

► Comparing F distributions ► Comparing three or more means 325► Measuring sampling error ► Comparing variances


► The sample size is at least 5

► Both nP and n (1-P) are at least 30► A continuous distribution is used to approximate a discrete distribution

► The standard normal distribution is applied

Question No: 18 ( Marks: 1 ) - Please choose oneStem and leaf is more informative when data is :

► Equal to 100

► Greater Than 100

► Less than 100

► In all situations


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Question No: 19 ( Marks: 1 ) - Please choose oneThe branch of Statistics that is concerned with the procedures and methodology for obtaining

valid conclusions is called:

► Descriptive Statistics► Advance Statistics► Inferential Statistics

► Sampled Statistics

Question No: 20 ( Marks: 1 ) - Please choose oneWhich of the following is a systematic arrangement of data into rows and columns?

► Classification► Tabulation► Bar chart► Component bar chart


If you connect the mid-points of rectangles in a histogram by a series of lines that alsotouches the x-axis from both ends, what will you get?

► Ogive► Frequency polygon► Frequency curve► Historigram

Question No: 24 ( Marks: 1 ) - Please choose oneWhich one of the following statements is true regarding a population?

► It must be a large number of values► It must refer to people► It is a collection of individuals, objects, or measurements► It is small part of whole


When1 32 4Q and Q

,what is the value of Median, if the distribution is symmetrical:

► 1► 2► 3► 4


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Question No: 26 ( Marks: 1 ) - Please choose oneIn a simple linear regression model, if it is assumed that the intercept parameter is equal

to zero, then:► The regression line will pass through the origin

► The regression line will pass through the point (0,10).► The regression line will pass through the point (0,-10).► The slope of the line will also be equal to 0.

Question No: 27 ( Marks: 1 ) - Please choose oneThe degrees of freedom for a t-test with sample size 10 is:

► 5► 8► 9► 10

Sample size refer to n and n=10= n-1=10-1=9Question No: 28 ( Marks: 1 ) - Please choose oneIn testing of hypothesis, we always begin it with assuming that:

► Null hypothesis is true► Alternative hypothesis is true► Sample size is large► Population is normal

Question No: 29 ( Marks: 1 ) - Please choose oneA failing student is passed by an examiner is an example of:

► Type I error

► Type II error

► Correct decision

► No information regarding student exams


How to find( 1)P X Y

?► f(0, 0) + f(0, 1) + f(1, 2) less than 1 or equal to 1 but it include 2 ► f(2, 0) + f(0, 1) + f(1, 0) its also include 2► f(0, 0) + f(1, 1) + f(1, 0) ► f(0, 0) + f(0, 1) + f(1, 0) pg 201 same as same


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Question No: 31 ( Marks: 2 )How many parameters are involved in hyper geometric distribution?

Answer = Three parameter n,N,K

Question No: 32 ( Marks: 2 )If an automobile is driven on the average no more than 16000 Km per year, then

formulate the null and alternative hypothesis.

AnswerNull hypothesis

0 : 16000

1: 16000

Halternative

H

Question No: 33 ( Marks: 2 )Write down the test statistic when chi- square goodness of fit test is performed.

Question No: 34 ( Marks: 3 )

Find the value of F(table value), when 1n 7 , 2n 10 and α= 0.05N1= 7-1=6N2=10-1=9The value of 6 in z table isThe value of (6,9)is 4.07The value of (9,6) is 3.37


If X = 327, n = 634,0p

0.50 then find the z-test statistic for proportion.

Question No: 36 ( Marks: 3 )If population proportions are given as:

Find1 2

2ˆ ˆp p

,where n = 10

Question No: 37 ( Marks: 5 )A candidate for mayor in a large city hires the services of a poll-taking organization, and

1 20.30, 0.20.P P


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they found that 62 of 100 educated voters interviewed support the candidate, and 69 of150 uneducated voters support him.At the 0.05 significance level, test the following

1 2: 0.05oH P P

1 1 2: 0.05H P P

Question No: 38 ( Marks: 5 )If we have RCBD with MSE=3.19, no.of.treatments = 4, no.of.blocks = 5; then find the

value of LSD (least significant difference) for treatments by using α=0.05 and errordegrees of freedom is 12.

Question No: 39 ( Marks: 5 )Find the mean and variance for the sampling distribution given below.

p No. ofSamples

Probabilitypf

0 1 1/201/3 9 9/202/3 9 9/201 1 1/20

20 1


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Paper 3

FINALTERM EXAMINATIONFall 2009

STA301- Statistics and Probability (Session - 1)Time: 120 min

Marks: 70

Question No: 1 ( Marks: 1 ) - Please choose one10! =………….

► 362880► 3628800► 362280► 362800

Write the number 10 in scientifice calculator than press shift and find the button !Question No: 2 ( Marks: 1 ) - Please choose one

When E is an impossible event, then P(E) is:

► 2► 0► 0.5► 1


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Question No: 3 ( Marks: 1 ) - Please choose oneThe value of χ2can never be :


Question No: 4 ( Marks: 1 ) - Please choose oneThe curve of the F- distribution depends upon

► Degrees of freedom pg 217► Sample size► Mean► Variance



is equal to:

► ) (E X E Y

► ) (E X E Y

► X E Y

► E X Y

Question No: 6 ( Marks: 1 ) - Please choose oneIn testing hypothesis, we always begin it with assuming that:




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For the Poisson distribution P(x) =

0.135 10.1351!

lthe mean value is :

►2► 5►10►0.135

Question No: 8 ( Marks: 1 ) - Please choose oneWhen two coins are tossed simultaneously, P (one head) is:

►

14

►

► ► 1

{HH,HT,TH,TT}Question No: 9 ( Marks: 1 ) - Please choose one

From point estimation, we always get

► Single value pg 262

► Two values

► Range of values

► Zero


The sample variance2

2 ( )x xSn

is:

► Unbiased estimator of 2

► Biased estimator of 2


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► Unbiased estimator of

► None of these

Question No: 11 ( Marks: 1 ) - Please choose oneVar(4X + 5) =__________

► 16 Var (X)► 16 Var (X) + 5► 4 Var (X) + 5► 12 Var (X)

Question No: 12 ( Marks: 1 ) - Please choose oneWhen f (x, y) is bivariate probability density function of continuous r.v.'s X and Y, then

,f x y dx dy

is equal to:

► 1 pg 203► 0► -1►


► .0401

► .5500

► .4599► .9599

Question No: 14 ( Marks: 1 ) - Please choose oneWhen a fair die is rolled, the sample space consists of

► 2 outcomes► 6 outcomes► 36 outcomes


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► 16 outcomes

Question No: 15 ( Marks: 1 ) - Please choose oneWhen testing for independence in a contingency table with 3 rows and 4 columns, there

are ________ degrees of freedom.► 5► 6► 7► 12

r-1*c-1=3-1=24-1=32*3=6Question No: 16 ( Marks: 1 ) - Please choose oneThe F- test statistic in one-way ANOVA is:

► SSW / SSE ► MSW / MSE ► SSE / SSW► MSE / MSW not sure


► The sample size is at least 5► Both nP and n (1-P) are at least 30► A continuous distribution is used to approximate a discrete distribution

► The standard normal distribution is applied

Question No: 18 ( Marks: 1 ) - Please choose oneA uniform distribution is defined by

► Its largest and smallest value► Smallest value

► Largest value► Mid value

Question No: 19 ( Marks: 1 ) - Please choose oneWhich graph is made by plotting the mid point and frequencies?

► Frequency polygon pg 30 book

► Ogive


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► Histogram

► Frequency curve

Question No: 20 ( Marks: 1 ) - Please choose oneIn a set of 20 values all the values are 10, what is the value of median?

► 2► 5► 10► 20

10,10,10,10,10,10,10,10,10,10,10Question No: 21 ( Marks: 1 )

If 0P X

=

18

, 1P X

=

38

, 2P X

=

38

and( 3)P X

=

18

Then find F (1)

Question No: 22 ( Marks: 2 )Write down the formula of mathematical expectation.

e=(w * p) + (-v *1). e

Question No: 23 ( Marks: 3 )Discuss the statistical independence of two discrete random variables:

http://vustudents.ning.comQuestion No: 24 ( Marks: 3 )For given data calculate the mean and standard deviation of sampling distribution of

mean if the sampling is down without replacement.

1000, 25, 68.5, 2.7N n

Question No: 25 ( Marks: 3 )Elaborate the Least Significant Difference (LSD) Test.



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State the Bayes’ Theorem.

Question No: 27 ( Marks: 5 )The means and variances of the weekly incomes in rupees of two samples of workers are

given in the following table, the samples being randomly drawn from two differentfactories:

Calculate the 90% confidence interval for the real difference in the incomes of theworkers from the two factoriesAnswer pg 271

.


From the given data1340, 723, .54n x p

and0 0 1 0: 0.5 : 0.5H P against H P

.Carry out the significance test for the stated hypothesis.


Factory Sample Size Mean VarianceA 160 12.80 64B 220 11.25 47


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Given the Probability density function.

Compute the distribution function F(x).Answer

Question No: 30 ( Marks: 10 )1f(x,y) (6 – x – y), 0 x 2; 2 y 4,80, elsewhere

a) Verify that f(x,y) is a jointdensity function.

b) Calculate

,25

Y,23

XP


Let1 2 3, ,X X X

be a random sample of size 3 from a population with mean2and variance

Consider the following two estimators of the mean

1 2 31

1 2 32

32

4

X X XT

X X XT

Which estimator should be preferred?AnswerSolution:First we examine which one among T1 & T2 is unbiased. If ONLY one of them is theunbiased we can prefer it as a better estimator. If both of them are unbiased then we have

elsewhere

xforxf

x

,0

20,2


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to compare their variances. The estimator with least variance will be the preferred.So let’s first see unbiasedness:T1 is sample mean X , which we know is unbiased.And for T2

1 2 32

2

2( )

41 4( ) ( 2 )4 4

X X XE T E

E T E

So T2 is also unbiased.Since both estimator are unbiased, NOW we have to check there variances.

1 2 31 1 2 3

2 22 2 2

1 2 32 1 2 3

2 22 2 2

1( ) ( ) ( ) ( )3 9

319 9 3

2 1( ) ( ) 4 ( ) ( )4 16

6 31 416 16 8

X X XVar T Var Var X Var X Var X

X X XVar T Var Var X Var X Var X

Comparing both variances

1 2

1 33 8

( ) ( )

so

Var T Var T

Hence we conclude that since T1 is unbiased as well as has low variance, so this estimatorT1 is better then T2.

Paper 4

FINALTERM EXAMINATIONFall 2009STA301- Statistics and ProbabilityTime: 120 minMarks: 70Question No: 1 ( Marks: 1 ) - Please choose oneIn measures of relative dispersion unit of measurement is:► Changed


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► Vanish ► Does not changed ► Dependent Question No: 2 ( Marks: 1 ) - Please choose oneThe location of the critical region depends upon:► Null hypothesis ► Alternative hypothesis pg 286► Value of alpha ► Value of test-statisticQuestion No: 3 ( Marks: 1 ) - Please choose oneThe F-distribution always ranges from:► 0 to 1 ► 0 to -∞► -∞to +∞► 0 to +∞Question No: 4 ( Marks: 1 ) - Please choose oneIn chi-square test of independence the degrees of freedom are:► n - p► n - p-1► n - p- 2► n – 2Question No: 5 ( Marks: 1 ) - Please choose oneFor a particular data the value of Pearson’s coefficient of skewness is greater then zero. Whatwill be the shape of distribution?► Negatively skewed ► J-shaped► Symmetrical ► Positively skewed Question No: 6 ( Marks: 1 ) - Please choose oneIf X and Y are random variables, then is equal to: E X Y► ) (E XEY► ) (E XEY ► X E Y ► E X Y Question No: 7 ( Marks: 1 ) - Please choose oneIf ŷis the predicted value for a given x-value and b is the y-intercept then the equation of aregression line for an independent variable x and a dependent variable y is:► ŷ = mx + b, where m = slope► x = ŷ + mb, where m = slope ► ŷ = x/m + b, where m = slope ► ŷ = x + mb, where m = slope Question No: 8 ( Marks: 1 ) - Please choose oneThe Chi- Square distribution is continuous distribution ranging from:► -∞≤χ2≤∞► -∞≤χ2 ≤1


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► -∞≤χ2 ≤0► 0 ≤ χ2≤∞pg 313Question No: 9 ( Marks: 1 ) - Please choose oneThe variance of the t-distribution is give by the formula:► 2 2 ► 2 2 2 ► 1 2 ► 2 2 Question No: 10 ( Marks: 1 ) - Please choose oneWhich one is the correct formula for finding desired sample size?► 2 2 . Z n e ► 2 2 . Z n e ► 2 2 .Z X n e ► 2 . Z n eQuestion No: 11 ( Marks: 1 ) - Please choose oneA discrete probability function f(x) is always:► Non-negative► Negative ► One► Zero Question No: 12 ( Marks: 1 ) - Please choose oneE(4X + 5) =__________► 12 E (X) ► 4 E (X) + 5► 16 E (X) + 5 ► 16 E (X) Question No: 13 ( Marks: 1 ) - Please choose oneHow P(X + Y < 1) can be find:► f(0, 0) + f(0, 1) + f(1, 2) ► f(2, 0) + f(0, 1) + f(1, 0)► f(0, 0) + f(1, 1) + f(1, 0) ► f(0, 0) + f(0, 1) + f(1, 0)Question No: 14 ( Marks: 1 ) - Please choose oneThe __________: |1 f x► 1,1 f ► ,1 f x► ,1 1 f x h


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► ,1 f xh x Question No: 15 ( Marks: 1 ) - Please choose oneThe area under a normal curve between 0 and -1.75 is► .0401 ► .5500 ► .4599► .9599 Question No: 16 ( Marks: 1 ) - Please choose oneIn normal distribution M.D. =► 0.5 ► 0.75 ► 0.7979 ► 0.6445 Question No: 17 ( Marks: 1 ) - Please choose oneIn an ANOVA test there are 5 observations in each of three treatments. The degrees offreedom in the numerator and denominator respectively are.......► 2, 4 ► 3, 15 ► 3, 12 ► 2, 12

3-1=25*3=1515-3=12

Question No: 18 ( Marks: 1 ) - Please choose oneA set that contains all possible outcomes of a system is known as► Finite Set ► Infinite Set ► Universal Set ► No of theseQuestion No: 19 ( Marks: 1 ) - Please choose oneStem and leaf is more informative when data is :


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► Equal to 100► Greater Than 100► Less than 100► In all situationsQuestion No: 20 ( Marks: 1 ) - Please choose oneA population that can be defined as the aggregate of all the conceivable ways in which a specifiedevent can happen is known as:► Infinite population► Finite population► Concrete population► Hypothetical population pg 12Question No: 21 ( Marks: 1 ), what do you say about the estimator T, where is a parameter ? () If ETQuestion No: 22 ( Marks: 2 )What is a binomial experiment?Question No: 23 ( Marks: 3 )Formulate the null and alternative hypothesis in each of the following.(1) Average domestic consumption of electricity is 50 units per month.(2) Not more than 30% people pay Zakat (tax).Question No: 24 ( Marks: 3 )What is mathematical expectation of discrete random variable?Question No: 25 ( Marks: 3 )Why we prefer to use pooled estimator c pQuestion No: 26 ( Marks: 3 )


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Differentiate between grouped and ungrouped data.Question No: 27 ( Marks: 5 )A random sample of size n is drawn from normal population with mean 5 and variance .Answer the following: 2If s=15, =14 and t=3, what is values of n? xQuestion No: 28 ( Marks: 5 )A population 2, 4, 6, 8, 10, 12N=6, n=2After drawing possible samples, we have calculated sampling mean and sampling variance .Verify 7 x u 2 5.833 x 2 2 ) , ) x x a b nQuestion No: 29 ( Marks: 5 )Given the Probability density function. elsewhere x for x f x , 02 0 , 2Compute the distribution function F(x).Question No: 30 ( Marks: 10 )A research worker wishes to estimate the mean of a population using a sample sufficientlylarge that the probability will be 0.95 that the sample mean will not differ from the true meanby more than 25 percent of the standard deviation. How large a sample should be taken?Question No: 31 ( Marks: 10 )An urn contains nine balls; five of them are red and four blue. Three balls are drawn withoutreplacement. Find the distribution of X= number of red balls drawn.

Paper 5

FINALTERM EXAMINATIONSpring 2010

STA301- Statistics and Probability (Session - 4)

Time: 90 minMarks: 60

Question No: 1 ( Marks: 1 ) - Please choose oneThe value of χ2can never be :




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►

22 1

1

1

forvv

v

►

22 2

2

2

forvv

v

►

22 1

1

1

forvv

v

►

22 1

2

2

forvv

v

Question No: 3 ( Marks: 1 ) - Please choose oneThe F-distribution always ranges from:

► 0 to 1 ► 0 to -∞► -∞to +∞► 0 to +∞

Question No: 4 ( Marks: 1 ) - Please choose oneThe total number of samples when sampling is done with replacement :

► nN

► NnC

► 1

N nN

► 1

Question No: 5 ( Marks: 1 ) - Please choose oneANOVA was introduced by :

► Helmert► Pearson► R.A Fisher► Francis


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Question No: 6 ( Marks: 1 ) - Please choose oneThe test statistic used in analysis of variance procedure follow the ....... distribution.:

► χ2

► T► Z► F

Question No: 7 ( Marks: 1 ) - Please choose oneFor testing of hypothesis about population proportion , we use:

► Z-test► t-Test► Both Z & T-test► F test



is equal to:

► ) (E X E Y

► ) (E X E Y

► X E Y

► E X Y

Question No: 9 ( Marks: 1 ) - Please choose oneA die is rolled. What is the probability that the number rolled is greater than 2 and even:

► 1/2► 1/3► 2/3► 5/6

Sample space={1,2,3,4,5,6,}Greater than 2 and even= {2,3,4,5,6,}5/6



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The probability of drawing a king of spade from a pack of 52 cards is:► 1/4► 1/13► 1/26► 1/52



► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1

Question No: 12 ( Marks: 1 ) - Please choose oneFrom point estimation, we always get:

► Single value

► Two values

► Range of values

► Zero


The best unbiased estimator for population variance2

is:

► Sample mean

► Sample median

► Sample proportion

► Sample variance


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Question No: 14 ( Marks: 1 ) - Please choose oneWhen c is a constant, then E(c) is:

1

0

c

-c

Question No: 15 ( Marks: 1 ) - Please choose oneVar(4X + 5) =__________

► 16 Var (X)► 16 Var (X) + 5► 4 Var (X) + 5► 12 Var (X)

Question No: 16 ( Marks: 1 ) - Please choose oneWhen f(x) is continuous probability function, then P(X = 1) is:

► 1►

► ► 0 pg 192

Question No: 17 ( Marks: 1 ) - Please choose oneThe hyper geometric random variable is a(an):

► Continuous variable

► Discrete variable

► Undefined

► Independent variable


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Question No: 18 ( Marks: 1 ) - Please choose oneFrom a sample of 200 people were asked whether they like a particular product. Fifty

said 'yes' and remain said 'no', assuming ‘yes’ means a success, which of the following iscorrect?

► Sample proportion p=0.33

► Sample proportion p=0.25

► Population proportion p= 0.33

► Population proportion p=0.25


In any data set, what percent of values fall in the interval.Median Q D ?

► 50 per cent► 68.5 per cent► 95.4 per cent► 99 per cent


If

5

1

20 0, .......ii

X then X

► 0► 20► 5► 25

Question No: 21 ( Marks: 1 ) - Please choose oneThe height of a student is 60 inches. This is an example of ...........?

► Continuous data► Qualitative data► Categorical data

► Discrete data


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Question No: 22 ( Marks: 1 ) - Please choose oneIn Statistics, we have MSE which is abbreviation of……

► Mean square error 335

► Measured square error

► Medical screening exam

► Major sampling error

Question No: 23 ( Marks: 1 ) - Please choose oneWhich one is the formula of mid range:

► 0mx x

► 0 mx x

►

0

2mx x

pg 81

►

0

2mx x

Question No: 24 ( Marks: 1 ) - Please choose oneThe deviation of a distribution from symmetry is called:

► Kurtosis► Skewness► Dispersion► Flatness

Question No: 25 ( Marks: 1 ) - Please choose oneIf E is an impossible event, then P(E) is:

► 1

► 2► 0► 0.5



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If a data set has the even number of observations, the median :► Is the average value of the two middle items

► Can not be determined

► must be equal to the mean

► Is the average value of the two middle items when all items are arranged in ascendingorder


For the Poisson distribution

0.135 10.135( 1)

1!e

P X

the mean value is :

► 2► 5

► 10► 0.135

Question No: 28 ( Marks: 1 ) - Please choose oneIn testing of hypothesis, we always begin it with assuming that:


Question No: 29 ( Marks: 1 ) - Please choose oneVariance of the t-distribution is given by the formula:

► 2

2

► 2

22

► 1

2


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► 2

2

pg 299


If a continuous probability distribution has2 2.14

then what will be peakedness of thedistribution?

► Platykurtic pg 117► Mesokurtic► Leptokutic► Moderately skewed

Question No: 31 ( Marks: 2 )What is the mean and variance of Poisson distribution?

Question No: 32 ( Marks: 2 )Explain the Chi-square test of goodness of fit.

Question No: 33 ( Marks: 2 )Define level of significance?


Find the value of F(table value), when 1n 7 , 2n 10 and α= 0.05

Question No: 35 ( Marks: 3 )Define Null and Alternative hypothesis.

Question No: 36 ( Marks: 3 )A random sample of 100 is taken from a population with mean 30 and standard deviation

5. The probability distribution of the parent population is unknown, find the mean and

standard error of the sampling distribution of X .

Question No: 37 ( Marks: 5 )What is the probability that a poker hand of 5 cards contain exactly 2 aces (hypergeometric

distribution)?


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Question No: 38 ( Marks: 5 )A random sample of size n is drawn from normal population with mean 5 and

variance2 .

If n=25, s=10 and t=2, what is the values of x ?

Question No: 39 ( Marks: 5 )Describe the main steps of General Procedure for Testing Hypothesis.

Paper 6

Question No: 1 ( Marks: 1 ) - Please choose oneFor a particular data the value of Pearson’s coefficient of skewness is greater then zero.

What will be the shape of distribution?

► Negatively skewed

► J-shaped

► Symmetrical

► Positively skewed

Question No: 2 ( Marks: 1 ) - Please choose oneIn measures of relative dispersion unit of measurement is:

► Changed ► Vanish ► Does not changed ► Dependent

Question No: 3 ( Marks: 1 ) - Please choose oneThe F-distribution always ranges from:

► 0 to 1 ► 0 to -∞


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► -∞to +∞► 0 to +∞

Question No: 4 ( Marks: 1 ) - Please choose oneIn chi-square test of independence the degrees of freedom are:

► n - p► n - p-1► n - p- 2► n – 2

Question No: 5 ( Marks: 1 ) - Please choose oneThe Chi- Square distribution is continuous distribution ranging from:

► -∞≤χ2≤∞► -∞≤χ2≤1► -∞≤χ2≤0► 0 ≤ χ2≤∞



is equal to:

► ) (E X E Y

► ) (E X E Y

► X E Y

► E X Y

Question No: 7 ( Marks: 1 ) - Please choose oneIf ŷis the predicted value for a given x-value and b is the y-intercept then the equation of

a regression line for an independent variable x and a dependent variable y is:

► ŷ = mx + b, where m = slope► x = ŷ + mb, where m = slope► ŷ = x/m + b, where m = slope

► ŷ = x + mb, where m = slope



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The location of the critical region depends upon:

► Null hypothesis► Alternative hypothesis► Value of alpha► Value of test-statistic

Question No: 9 ( Marks: 1 ) - Please choose oneThe variance of the t-distribution is give by the formula:

► 2

2

► 2

22

► 1

2

► 2

2

Question No: 10 ( Marks: 1 ) - Please choose oneWhich one is the correct formula for finding desired sample size?

►

2

2.Z

ne

►

2

2.Z

ne


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►

2

2.Z X

ne

►

2.Z

ne

Question No: 11 ( Marks: 1 ) - Please choose oneA discrete probability function f(x) is always:

► Non-negative► Negative► One► Zero

Question No: 12 ( Marks: 1 ) - Please choose oneE(4X + 5) =__________

► 12 E (X)► 4 E (X) + 5► 16 E (X) + 5► 16 E (X)

Question No: 13 ( Marks: 1 ) - Please choose oneHow P(X + Y < 1) can be find:


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► f(0, 0) + f(0, 1) + f(1, 2)► f(2, 0) + f(0, 1) + f(1, 0)► f(0, 0) + f(1, 1) + f(1, 0)► f(0, 0) + f(0, 1) + f(1, 0)


The |1f x

__________:

► 1,1f

► ,1f x

►

,11

f xh

►

,1f x

h x


► .0401

► .5500

► .4599► .9599

Question No: 16 ( Marks: 1 ) - Please choose oneIn normal distribution M.D. =

► 0.5

► 0.75

► 0.7979


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► 0.6445

Question No: 17 ( Marks: 1 ) - Please choose oneIn an ANOVA test there are 5 observations in each of three treatments. The degrees of

freedom in the numerator and denominator respectively are.......► 2, 4► 3, 15► 3, 12 ► 2, 12


A set that contains all possible outcomes of a system is known as

► Finite Set

► Infinite Set► Universal Set

► No of these

Question No: 19 ( Marks: 1 ) - Please choose oneStem and leaf is more informative when data is :

► Equal to 100

► Greater Than 100

► Less than 100

► In all situations

Question No: 20 ( Marks: 1 ) - Please choose oneA population that can be defined as the aggregate of all the conceivable ways in which a

specified event can happen is known as:

► Infinite population► Finite population► Concrete population► Hypothetical population



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( )If E T , what do you say about the estimator T, where is a parameter ?

Question No: 22 ( Marks: 2 )What is a binomial experiment?

Question No: 23 ( Marks: 3 )Formulate the null and alternative hypothesis in each of the following.

(1) Average domestic consumption of electricity is 50 units per month.(2) Not more than 30% people pay Zakat (tax).

Question No: 24 ( Marks: 3 )What is mathematical expectation of discrete random variable?


Why we prefer to use pooled estimatorcp

Question No: 26 ( Marks: 3 )Differentiate between grouped and ungrouped data.

Question No: 27 ( Marks: 5 )A population 2, 4, 6, 8, 10, 12

N=6, n=2

After drawing possible samples, we have calculated sampling mean7xu

and sampling

variance

2 5.833x . Verify

22) , )x xa b

n

Question No: 28 ( Marks: 5 )A random sample of size n is drawn from normal population with mean 5 and

variance2 . Answer the following:

If s=15, x =14 and t=3, what is values of n?


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Question No: 29 ( Marks: 5 )Given the Probability density function

.

Compute the distribution function F(x).

Question No: 30 ( Marks: 10 )An urn contains nine balls; five of them are red and four blue. Three balls are drawn

without replacement. Find the distribution of X= number of red balls drawn.

Question No: 31 ( Marks: 10 )A research worker wishes to estimate the mean of a population using a sample

sufficiently large that the probability will be 0.95 that the sample mean will not differfrom the true mean by more than 25 percent of the standard deviation. How large asample should be taken?

Paper 7

Question No: 1 ( Marks: 1 ) - Please choose oneA five-number summary consists of :

► X0, Q1, Median, Q3, and Xm

► Xm, Q1, Mean, Q3, and X0

► Xm, Q1, Mode, Q3, and X0

► X0, Q1, Median, Q2, and Xm

Question No: 2 ( Marks: 1 ) - Please choose oneWhich is appropriate average for finding the average speed of a car:

► Mean► Geometric mean► Harmonic mean► Weighted mean

elsewhere

xforxf

x

,0

20,2


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Question No: 3 ( Marks: 1 ) - Please choose oneWhat is the probability of sure event:

► 0► 1► 0.5► 2

the probability of a sure event is 1. i.e. P(S) = 1.Question No: 4 ( Marks: 1 ) - Please choose oneIn positively skewed distribution, which of the following relationship exists:

► The mean, median, and mode are all equal► The mean is larger than the median► The median is larger than the mean► The standard deviation must be larger than the mean or the median

Question No: 5 ( Marks: 1 ) - Please choose oneWhen two coins are tossed the probability of at most one head is:

► 1/4► 2/4► 3/4► 4/4{HH,HT,TH,TT}

Tt,th,ht

Question No: 6 ( Marks: 1 ) - Please choose oneThe number of ways in which four books can be arranged on a shelf is:

► 4► 6► 12► 24

4x3x2x1=24 or alternative 4!=24

Question No: 7 ( Marks: 1 ) - Please choose oneStandard deviation of the data 7, 7, 7, 7, 7, 7, 7 is

► 49► Sqrt (7)► 0► 7

The mean of 7 number is 7 when we subtraction mean 7 from above observation weget 0


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Question No: 8 ( Marks: 1 ) - Please choose oneThe sum of deviations is zero, when deviations are taken from:

► Mean► Median

► Mode► H.M


In a symmetrical distribution, if1 2 320, 30Q Q then Q is

:► 50► 40► 30► 10

Question No: 10 ( Marks: 1 ) - Please choose oneThe Zip-Code of a city is an example of:

► Qualitative data► Discrete data► Quantitative data► Continuous data

Question No: 11 ( Marks: 1 ) - Please choose oneA histogram is consists of a set of adjacent rectangles whose bases are marked off by?

► Class boundaries pg 32

► Class limits

► Class marks

► Class frequency

Question No: 12 ( Marks: 1 ) - Please choose oneWhat is the value of class mark for the given class 20-24?

► 20


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► 24► 22► 44

20+24=4444/2=22

Question No: 13 ( Marks: 1 ) - Please choose oneWhat we commonly called a bell shaped distribution?

► Symmetrical► Bimodal► Skewed► U shaped

Question No: 14 ( Marks: 1 ) - Please choose oneWhen the values are equally distributed at the both sides from the center, then it is

► Symmetrical distribution► Positively skewed► Negatively skewed► U shape figure

Question No: 15 ( Marks: 1 ) - Please choose oneWhen mean is equal to mode, then the distribution is:

► Symmetrical► Skewed to the right► Skewed to the left► Negatively skewed



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While making a frequency distribution, among the following, which step comes at the last?

► Class interval

► Range

► Tally

► Class groups

Question No: 17 ( Marks: 1 )What is the probability of an even number selected at random form the following elements?

Question No: 18 ( Marks: 1 )Define the term Event.

Question No: 19 ( Marks: 2 )What is coefficient of determination?

Question No: 20 ( Marks: 3 )What is the difference between a sample space and event space?

Question No: 21 ( Marks: 5 )For 2 roll of a balanced die, find the probability of getting “first a number 5 AND then a number

less than or equal to 3”.Ans:

Stat final informationTotal question 31

Year 2010

1) question from confidence interval , question was of 3 marks,


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find the confidence interval for difference between two ( papolation means) u1 ,u2,2) question from hypotheses testing ( Z- test) , marks 103) questions was about properties, one was, write the properties of binomial distribution.and other was ,

what is the good point estimator?4) question was from lecture no 23 , this was of 3 marks

page no 172, 1st example was same to same.find the F(x) of { 1, 2}

x and f( x) was given.

Definition estimate n estimator

Statistics 2011final term informationPAPER#1

Share by someone1: Define binomial random variable. 22: Eleborate poisson distribution. 23: Write some advantages and short coming of frequency distribution. 34: one question is about chi-square. 2

PAPER#2

is s12 is 244.14 ans s22 is 124 then find F-Distribution(marks 2)if n=4, u=2 then find P of bionomial distribution (marks 3)define Centeral Limit theorem (marks 5)S(y,x) find out kerna tha (marks 5)Confidence Interval ka aik question tha (marks =5)goodness of fit test (marks 5)

MCQs


is equal to:

Ideally the width The |1f x

__________:

of confidence interval should be

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Composed & Solved Armaan Makhani Vu Askari Team www ...api.ning.com/files/Gl0rHpgzlOlopl2r97jc1nDcVLxkgrOITaIgXHfUQUI55Q4w3Y9... · Composed & Solved Armaan Makhani Vu Askari Team