Inter (Part-II) Lahore Board 2013
Statistics
Paper: II
(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.

Question#1

• Regression coefficient is independent of:
  
  (A) Units of measurement
  (B) Scale and origin
  (C) Scale only
  (D) Both A and B
  
  
• The value of x2 statistics is always:
  
  (A) Positive
  (B) Negative
  (C) One 
  (D) Zero
  
  
• In sampling without replacement, an element can be chosen:
  
  (A) More than twice
  (B) More than once
  (C) Less than once
  (D) Only once
  
  
• When the production of a thing is decreasing, this stage is called as:
  
  (A) Recession 
  (B) Recovery
  (C) Boom
  (D) Depression
  
  
• The probability of rejecting Null Hypothesis when it is false is:
  
  (A) Error
  (B) Type I error
  (C) Type - II error
  (D) Power of test
  
  
• The sum of squares of residuals is denoted by:
  
  (A) e
  (B) e
  (C) e2
  (D)
  
  
• A population about which we want to get some information is called:
  
  (A) Finite population 
  (B) Infinite population
  (C) Sample population
  (D) Target population
  
  
• For the standard normal distribution, P (Z > mean) is:
  
  (A) Less than 0.5
  (B) More than 0.5
  (C) Equal to 0.5 
  (D) Equal to one
  
  
• The value of rxy is always between:
  
  (A) -1 and +1 
  (B) -  and 0
  (C) 0 and +1   
  (D) = and +
  
  
• If (AB)= –, the two attributes A and B are:
  
  (A) Independent
  (B) correlated
  (C) Dependent
  (D) Quantitative
  
  
• If the magnitude of calculated value of "t" is less than the tabulated value of "t" two sided, we should:
  
  (A) Reject H_o
  (B) Not reject H_o
  (C) Reject H₁
  (D) Accept H₁
  
  
• f(x) dx is always equal to:
  
  (A) Zero
  (B) One
  (C) E(x)
  (D) f(x) + 1
  
  
• An estimator 0 is said to be unbiased estimator of 0 if:
  
  (A) E () = θ
  (B) E ()> θ
  (C) E ( ) < θ
  (D) E ()  θ
  
  
• The term sample space is used for
  
  (A) All possible outcomes
  (B) Sample
  (C) Probability
  (D) Sample design
  
  
• In the regression equation X = a + by, X is called:
  
  (A) Dependent variable
  (B) Independent variable
  (C) Qualitative variable
  (D) Quantitative variable
  
  
• Printer, monitor, scanner and plotter are the:
  
  (A) Input devices
  (B) Output devices
  (C) Processing devices
  (D) Storage devices
  
  
• If X is N(µ,σ²), the percentage of the area contained within the limitsµ. ± 3 a is:
  
  (A) 50% 
  (B) 68.27%
  (C) 95.45%
  (D) 99.73%

Inter (part-II) Lahore Board 2013
Statistics
Paper: II (Essay type)
Time: 2:40 Hours
Marks: 68
(Section - I)  

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

• Define normal distribution.
• Write down any three properties of the normal curve.
• Write down the equation of normal curve.
• What is relationship between the binomial distribution and normal distribution?
• Explain why β1 equals zero for the normal distribution.
• What is statistical inference?
• What is type-I error?
• Define level of confidence.
• What is test statistic?
• What is degrees of freedom?
• What is computer hardware?
• What is mini computer?

3. Write short answers to any EIGHT (8) questions: (16)

• Define sampling units.
• Distinguish between finite and infinite population.
• What is sampling?
• Explain term sampled population.
• Write any two advantages of sampling.
• Given N1 = 3 , n1= 2 , N2 = 4 , n2= 2,= and =. Find the value of
• Define simple linear regression.
• Explain the difference between fixed variable and random variable.
• Find the slope and y-intercept of the line whose equation is 3x -5y = 20.    
• Define simple correlation.
• Distinguish between positive and negative correlation.
  Given
  ∑(X - ) (Y- )= 0,∑(X -  )²= 10, ∑(Y - )² =10 and n = 5. Find the co-efficient of correlation.4.

4. Write short answers to any SIX (6) questions: 12

• What is historigram?  
• Give any two examples of cyclical variations.
• What is time series?
• Explain the two models of time series.
• Explain briefly about random variations by giving one suitable example.
• Write down four components of time series.
• Define a contingency table.
• What is an attribute?
• What is perfect positive association?

(Section – II)

Note: Attempt any THREE questions.
Question#5
(a) The mean height of army men is assumed to 69 inches and variance is 9 inches. How many soldiers in a regiment of 1000 soldiers would you expect be over 6 feet tall? 4
(b) In a normal distribution M.D. = 1.6, find: (i) σ (ii) µ2 (iii) Q.D. (iv) µ4. 4

Question#6
(a) From a population 9 & 3: 4
(i) Find all possible samples of size 3 with replacement and compute the mean of each sample.
(ii) Make the sampling distribution of sample means.
(b) (i) Find the mean and variance of the sampling distribution of means formed in part
(ii) above.
(iii) Verify that ;  .

Question#7
(a) If n1 =10   ₁= 20             =30
n2 = 20  ₂=15             = 25
Find 95% confidence interval for µ1-µ2. 4
(b) A sample of size 100 is taken from a population whose variance is 25. If sample mean is 50
Test 
Ho: µ=60
H1: µ 60
At α = 0.01    

Question#8 
(a) The number of units produced by a process 'X' and cost of producing unit 'Y' were made as:
N = 4 ∑ x = 20 ∑x² = 110 ∑y = 25 ∑y² = 162
∑ xy = 132
Find co-efficient of correlation "r". 4
(b) Fid the regression line from the following data of model = a + bx: 4