Statistics 
Lahore Board 2016 
Inter Part-II
Time: 20 Min.
7 Objective
Marks = 17
Note: Four possible answers A, B, C and D to each  question are given. The choice wh'ch you think is 
correct, fill that circle in front of that question with  Marker or Pen ink in the answer-book.Cutting or  filling two or more cir -les will result in zero mark in  that question.

• If HO is true and we reject it then it is called :

(A) Type I error
(B) Type II error
(C) Standard error
(D) Sampling error

• Ei One byte is equal to :

(A) 8 bits
(B) 4 bits
(C) 6 bits
(D) 12 bits          

• If rxy = 0.75 the correlation co-efficient between u=1.5x and v = 2y i.e. ruv, is:

(A) Zero
(B) 0.75
(C) - 0.75
(D) 1.5

• The range of normal distribution is :

(A) 0 to +∞
(B) -∞ to 0
(C) -∞ to + ∞
(D) 0 to n

• Which of the following is biased estimator . 

(A)  = 
(B) =
(c) S2 =  
(D) S2 =    

• When bxy is positive then byx will be :

(A) Negative
(B) Positive
(C) Zero
(D) One

• In a normal curve μ ± 2 σ covers :

(A) 50% area
(B) 68.27% area
(C) 95.45% area
(D) 99.73 % area

• A second degree parabola has

(A) One constant
(B) Two constants
(C) Three constants
(D) No constant

• A business cycle has 

(A) One stage
(B) Three stages
(C) Two stages
(D) Four stages

• If  = 10 and μ = 12 then sampling error is equal to:

(A) 22
(B) 10
(C) -2
(D) 12

• The value of the co-efficient of correlation “r” lines  between

(A) 0 and 1
(B) -1 and 0
(C) -1 and + 1
(D) -0.5 and + 0.5

• The shape of the curve of normal distribution is :

(A) Lepto-kurtic
(B) Platy-kurtic
(C) Skewed
(D) Meso-kurtic

• A hypothesis may be classified as:

(A) Simple
(B) Composite
(C) Null
(D) All of these

• The standard deviation of any sampling distribution is called :

(A) Standard errors
(B) Non-sampling error 
(C) Type-I error
(D) Biased error

• The order of (ABC) is:

(A) 1
(B) 3
(C) 2
(D) Zero

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

(A)   
(B)
(C)  
(D)  

• In sampling with replacement, the following is always true :

(A )n = N
(B) n<N
(C) n>N    
(D) All of these

Subjective
Section-I

2. Write short answers to any Eight (8) questions: (16)

1. Define the normal frequency distribution
   
2. In a normal distribution μ4 = 768 . find μ2
   
3. If XN (25. 25), find the value of maximum ordinate?
   
4. In a normal distribution the Q1 = 18 and Q3 =26. Find its mean and standard deviation.
   
5. Explain the statistical inference.
   
6. What is meant by unbiasedness?
   
7. Write a short note on critical region.
   
8. Define the central processing unit.
   
9. What is the relationship between the binomial distribution and the normal distribution?
   
10. If  = 100. σ = 8 and n = 64, .set up a 95% confidence  interval for μ?
    
11. 
    
12. What is meant by programming?
    
    3. Write short notes on any EIGHT (8) questions: (16)
13. Define finite and infinite population
    
14. Define sampling error.
    
15. Define parameter and statistic.
    
16. Define sampling with replacement.
    
17. Take all possible sample of size n = 2 without  replacement from the following population 2. 4. 6,                8.10
    
18. What is meant by bias?
    
19. Given  = 1,    = 2, b = 2 then find the value of a
    
20. Given byx = 0.85, bxy = 0.86 find
    
21. Give any two properties of the co-efficient of  correlation.
    
22. Write down the normal equation for y = a + bx and  x = c + dy.
    
23. Explain the method of least square.
    
24. Given Sxy= 90 ,  Sx =4.  Sy = 16 compute byx and  xy             

4. Write short answers to any SIX (6) questions:     

1. Define time series.
   
2. Explain the term secular trend.
   
3. Define signal.
   
4. Write the two advantages of the semi-average method.
   
5. Define the moving average method.
   
6. Define noise.
   
7. What is meant by attributes?
   
8. Define contingency table.
   
9. Given (AB) = 30  (A) = 40 ,  find (Aβ)

SECTION-II

Note: Attempt any THREE questions.

5.(a) For a normal distribution p = 50 and σ = 100 . find (i) P (X > 50)       (ii) P (X < 50) 
(b) If "Z" is N (0 ; 1) then find P(-2 < Z < + 2)?              
6. (a) Draw all possible samples of size "2" with replacement from the population 3. 7. 8 and 12. Verify                that
  
(b) A population consists of numbers 3, 4, 5, 6 and 8. Find the proportion of even numbers of the     samples of size"3 "without replacement and show that :      


7.(a) Obtain the best unbiased estimates of the population mean μ and variance σ2 from which the      following  sample is drawn : n = 8, ∑x = 120 ,  ∑(x-)2 = 302
(b) A random sample of n = 50 children, contain 6 left handed. Test the hypothesis   
H0 :π = vs.  H1 : π  

8.(a) For the data even below :

                Find the regression equation of y on X and hence estimate  Y if X = 12. Also prove that ∑(Y - )= 0
(b) For a set of 50 pairs of observation the standard deviations of X and Y are 4.5 and 3.5       respectively . the sum of product of deviation of X and Y values from their respective means is 420. Find Karl Pearson co-efficiant of correlation.

9.(a) Test the association between the subject and results from the following table

 (b) Find the trend values by method of least square:

 Also estimate the scale for 2000.

SECTION-III
(Practical Part)

Note:    Attempt any THREE questions.

(A) Draw all possible samples of size 2 without replacement from the  papulation:

Where M and S stand for married and single respectively.
(i) μp = π 
(ii) σ2 p  =   []

(B) Give the following values:

Calcutate  the value of ‘t’ statistic.

(C)  Determined the regression equation to the following data and show that   ∑ (y- ŷ) = 0

(D) Find the association between injection against typhoid and exemption from attack from the following contingency table

(E) Find out 4- year moving average (centered) for the given data: