Inter (Part-II)  
Lahore Board 2012
Statistics   
Paper I (Objective Type)
Time Allowed: 20 Minutes    
Max. Marks: 17

Note: Four possible answers A, B, C and D to-each question are given. The choice which you think is correct, fill that circle in front, of that question with Marker or Pen ink. Cutting or
filling two or more circles will result in zero mark in that question. Write the letter A, B, C or D in the column (write correct option) against each question also. If there is contradiction in the bubble and hand written answer, bubble option will be considered correct,

Q1.

• The normal curve is called
  

(A) Leptokurtic          
(B) Platykurtic           
(C) Mesokurtic          
(D) Skewed

• The area to the left of + a for a normal distribution is approximately equal to
  

(A) 0.16
(B) 0.34
(C) 0,50
(D) 0.84

• In a normal distribution, the value of 131 and 132 are respectively
  

(A) 0 and 3
(B) 3 and 0
(C) 0 and 1
(D) 1 and 3

• A survey conducted by a sampling design is called
  

(A) Population survey
(B.) Sample survey
(C) Systematic survey
(D) Pakistan survey

•  s2 = is called: 
  

(A) Population variance
(B) Biased population variance
(C)Unbiased sample variance
(D) Biased sample variance                             

• Probability sampling is also called
  

(A) Random sampling
(B) Non random sampling
(C) Biased sampling
(D) Judgment sampling                      

• is called en unbiased estimator of θ  if:

(A) E () < θ
(B) E () > θ
(C) E () ≠ θ
(D) E () = θ

• The confidence interval for μ when is known is given by

(A) X ± za/2
(B) X ± ta/2
(C) X ± za/2
(D) X ± ta/2 ix-

• The level of significance is denoted by                        
  

(A) 1-∝                      
(B) ∝              
(C)β                
(D) 1 - β

• When value of bxy is negative, then byx is
  

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

• The dependent variable is also called
  

(A) Regressor             
(B) Predictor  
(C) Predictand
(D) Continuous variable

• The value of correlation coefficient lies between
  

(A) – and + ∞           
(B) 0 and ∞   
(C) - ∞ and 0
(D) -1 and + 1

• The number of cells in a 4 3 contingency table are
  

(A) 5                          
(B) 12            
(C) 7              
(D) 1

• Two attributes A and B are independent if
  

(A) (AB)=
(B) (AB)<
(C) (AB)>
(D) (AB)≠

• The difference between the actual value and the trend value is called:
  

(A) Slope       
(B) Residual               
(C) Intercept             
(D) Sum of residual

• Decomposition of time series is called
  

(A) Time series
(B) Analysis of time series
(C) Detrending
(D) Descasonalization

• The first commercially available computer was
  

(A) Univac     
(B) Eniac                    
(C) Mark 1                 
(D) Analytical engine

SUBJECTIVE TYPE
SECTION-I

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

• Briefly describe the importance of the normal distribution.
  
• Discuss the relation between binomial and normal distribution.
  
• Give the equation of the normal curve with
  (a) mean μ and standard deviation 'S' . (b) mean 0 and variance 1.
  
• A normal distribution has mean 80 and variance 36, find mode, quartiles and median.
  
• In the normal distribution, the lower and upper quartiles are 8 and 17; find mean and standard deviation of the normal curve.
  
• Define the term point estimate and interval estimate.
  
• Explain what is meant by unbiased estimator.
  
• Why we call standard deviation of a sample statistic as standard error of the sample statistic? ix- What is meant by significant difference in hypothesis
  
• Distinguish between rejection and non-rejection regions.
  
• Define the term memory and storage.
  
• Describe low-level and high level languages.

3. Write short answers to any EIGHT (8) questions: 

• Define population and sample.
• What are basic aims of sampling?
• What is sample design?
• Differentiate between parameter and statistics.
• What is sampling distribution?
• What are advantages of sampling?
• What is regression?
• What is method of least squares?
• What is independent variable in regression?
• Define causation in correlation.
• Define negative correlation.
• Show that r =√(byx)(bxy)

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

• Explain rank correlation.
• Define attributes.
• If(A) = 20 (B)= 10 n = 40, find (AB)?
• Define analysis of time series.
• Explain cyclical variation.
• Explain free hand curve method.
• If y= 10 + 3x-, find the trend values for x=1,2,3,4?
• Estimate y for x 10 from the information n =5.  =0  = 20   = 62  2 =10
• What is multiplicative model (If time series?

           (SECTION - II)

Note: Attempt any THREE questions.

5.
(a) Let X~ N (40, 64), then find the single point which has 90% area below it.
(b) If X is normally distributed with mean = 25 and variance = 16, then find the probability:                                               (i)P (18 ≤ X ≤ 32)                  (ii) P(X ≥ 30)              (iii) P(X ≤ I 6)?

6.
(a) To compute standard deviation of statistic X (Sample Mean) take all possible samples of size two without replacement from the population 1, 3, 5, 5 and 7.
Verify that :  σx =  x                                            
(b) If population proportion (P) is 0.36, what would be μp, and σp? if several samples each of size 100 is drawn from the same population, where p is sample proportion?

7.
(a) Two random and independent simples of size n1 =11 and n2 = 14 from two normal populations give the following results:
X = 75 2 = 372.10
Y = 60 2 = 365.17
Find 99% confidence interval (μ1-  μ2)Assume that two population variances are equal, i.e., σ12= σ 22
(b) Ten students spend the following time hours of their studies during a week
35, 40, 17, 23, 50, 45, 30, 20, 18 and 22. Test the hypothesis μ ≤ 20 at α= 0.05

8.
(a) From the information given below
  = 150, S2x =64, S2y = 260, n=16
(i) Find the regression coefficients.
(ii) Determine the regression line X on Y_

(b) Find out the correlation coefficient for the following data of speed and time:

  Also interpret the result.

9.
(a) Compute rank correlation co-efficient from the following data :                                               

(b) Fit a straight line y = a + bx from the following results for the years (1948 - 58) both
=0  =438.9 2 =110 =84.4.
Also find the trend values.