RAWALPINDI BOARD 2012
 PAPER STATISTICS PART-II
Time: 20 Minutes     
(Objective Part)   
Marks: 17

Note:   Four Answers are given against each column A,B,C&D, Select the write answer and only separet answer sheet, fill the circle A, B,C or D with pen or marker in front of thatquestion number.

• The parameters of the normal distribution are:
  

(a) π & e                                
(b) π & p
(c) μ &                               
(d) e & μ

• In a normal distribution E(X - μ)2 is:
  

(a) Q.D                                   
(b) S.D       
(c) M.D                                  
(d) Variance

• If Z  N(0,1), then C.V
  

(a) 0                                       
(b)         
(c) 1                                        
(d)

• A numerical characteristic calculated from population is called:
  

(a) Sampling Unit                   
(b)Statistic
(c) Parameter                          
(d) Target Population

• When sampling is done with or without replacement E(1 - 2 is equal to:
  

(a)                             
(b)          
(c)                             
(d)

• If N = 4 and n = 3 in the simple random sampling with replacement, then possible samples are:
  

(a) 64                                     
(b) 16         
(c) 24                                     
(d) 4

• The formula that is used to estimate a parameter is called:
  

(a) Estimate                            
(b) Estimation         
(c) Bias                                   
(d) Estimator

• E() – 0 =
  

(a) Sampling Error                  
(b) Bias
(c) Non-Sampling Error         
(d) S.F

• When Ha : θ  θ0 then H0 is:
  

(a) 0 < θ0                                
(b) 0 > 0θ0
(c) 0  0θ0                              
(d) 0 = θ0

• The formula for `y ' is:
  

(a)                                  
(b)     
(c)                          
(d)

• When there is prefect positive correlation, then y =
  

(a) -1                                       
(b) +1        
(c) 0                                      
(d) 2

• The method of least squares is a process in which sum of squares of residuals is:
  

(a) Minimum                          
(b) Maximum             
(c) Zero                                 
(d) None

• Two attributes A and b are independent, if (AB) =
  

(a)                                     
(b)                
(c)                                  
(d) 

• Which of the following can never be rank orrelation:
  

(a) 0                                        
(b)        
(c) -1                                       
(d)

• The component of time series is:
  

(a) 2                                        
(b) 3         
(c) 4                                        
(d) 5

• Sales of stationery items in the start of academic session is example of:
  

(a) Trend                               
(b) Seasonal
(c) cyclical                              
(d) Irregular

• 01 byte is equal to:
  

(a) 4 bits                                 
(b) 6 bits    
(c) 8 bits                                
(d) 10 hits

Time: 2:40 Hours 
(Subjective Part) 
Marks: 68
SECTION-I

2. Write short answers of any Eight parts.                         16

• Find the fordinate at Z=0 of standard nonnal distribution.
• What is relationship between binomil distribution and normal distribution.
• In a normal distribution if µ = 163 and Q3171.094, Find the standard deviation. (iv) If Z is N(0,1).
• Find P(µ < Z < )         .
• Show that P(µ– 1.5 < X < µ + 1.5) = 0.8664
• Define a confidence interval.
• What is meant by critical value?
• Differentiate between acceptance and rejection region.
• What is meant by composite hypothesis?
• Describe general procedure for testing null hypothesis.
• Differentiate between assembler and compiler.
• Differentiate between hard copy and soft copy

3. Write short answers of any Eight parts.                         16

• Explain the term sampling deign,
• Write down two properties of sampling technique.
• Given µ=6,0=2,2=10.8.Find E(S2) .where S2 =∑(X1 –)2/n-1
• Differentiate between parameter and statistic.
• Explain the simple random sampling.
• What is the value of finite population correction factor, When n 18 and N-125'?
• Given X=2,4,6 and y=4,4,4. Find simple correlation co-efficients.
• Differentiate between perfect positive and perfect negative correlation.
• Write down two properties of correlation co-efficents.
• Explain the co-efficients of regression.
• Deline regression.               
• Define negative regression.

4. Write short answers of any Six parts.                             12

• Write a complete2 x2 contingency table for two attributes A and B.
• Given: A =20. B=80 and N 100. Find expected frequency of AB,if A and B, if A and B arc independent.
• What are the minimum and maximum values of coefficient of association?
• what is time series?            
• Explain method of semi-average.
• Write down four components of time series.
• Note names of the phases of business cycle.
• Write down three sourcess of irregular variation.
• Define principle of least square.

SECTION-II:

Attempt any THREE questions. Each questions carries 8 marks.

5.
(a) In a normal distribution µ = 30 and  = 5 .What proportion of cases will fall between 20 and 35?  04
(b) Suppose that X is normally distributed with µ = 25 and  = 5 Find:                                                 04

6.
(a) A population consist of values 2.4,6 and 8. Select all possible of size n=3 without replacement. Find
the standard error of means                                                                                                     04
(b) Given the following population distribution.                                                                                       04

1. Find proportion of even numbers in the population.
2. Find n when n=6 is drawn with replacement from the population.
3. Find p when n=2 is drawn without replacement from the population.

7.
(a) Find 90% confidence interval for p1 – p2 if: n1 =10, n2 = 20 and X1 = 6 , X2 = 8             04
(b) Test the null hypothesis H0 = µ1 =µ2 against H =µ1 µ2, if:04

8.
(a) From the following data, determine the regression line y=a+b X,        04

(b)     For a sample of 20 pairs of values, we have
X=2,∑y=160, ∑x2 =180, ∑y2 = 3424, ∑XY=604Calculate the correlation coeffiecient                                         

9.
(a) In a locality 300 persons were randomly selected and asked about their educational attainment the
results are given as follows

Can we say that the education depends on sex? Use a=0.05.
(b) Calculate 7 day moving average for the following record of attendance,   04