SARGODHA BOARD 2016
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 that question number.

Question#1

• In a normal distribution p =10 , a2 = 25 , the diode is:
  
  (a) 5   
  (b) 10 
  (c) 25 
  (d) 250
  
  
• The range of the normal distribution is:
  
  (a) 0 to       
  (b) 0 to n        
  (c) -co to  
  (d) None
  
  
• In a normal distribution µ3 is always:
  
  (a) < 0 
  (b) > 0
  (c) 0    
  (d) None
  
  
• In an infinite population µ = 50 2 = 250, n = 25 then variance () is:
  
  (a) 10  
  (b) 50  
  (c) 2.5 
  (d) None
  
  
• A population consists of 1, 2, 3, 4, 5 then the proportion of even numbers in the Population is:
  
  (a)
  (b)
  (c)
  (d) None
  
  
• The mean of the sampling distribution of sample mean (µ ) is equal to:
  
  (a)    
  (b) µ   
  (c) π.   
  (d) None
  
  
• The coefficient of correlation (r) always lies between:
  
  (a) -1 to 0       
  (b) 0 to -1       
  (c) -1 to +1
  (d) None
  
  
• If byx = -1 , bxy = -1 , then ryx is:
  
  (a) +1  
  (b) -1  
  (c) 0    
  (d) 0.5
  
  
• If byx is positive, then rxy will be:
  
  (a) Negative
  (b) Positive
  (c) 0    
  (d) None
  
  
• A single value used to estimate the population parameter is called:
  
  (a) Level of significance        
  (b) Point estimate
  (c) Interval estimate   
  (d) None
  
  
• The hypothesis which completely specifies the values of the parameters is called:
  
  (a) Null           
  (b) Simple
  (c) Alternative
  (d) Composite
  
  
• A Null hypothesis alwyas contains:
  
  (a) Equality sign         
  (b) Inequality sign
  (c) No sign     
  (d) None
  
  
• The value of λ2 may be:
  
  (a) -5   
  (b) -3  
  (c) -1   
  (d) >0
  
  
• For two independent attributes, the value of coefficient of association (Q) is:
  
  (a) +1  
  (b) -1  
  (c) Zero          
  (d) 2
  
  
• Decomposition of time series is called':
  
  (a) Time series
  (b) Analysis of time series
  (c) Detrending
  (d) None
  
  
• If a straight'line is fitted to time series, then:
  
  (a) ∑y = ∑y    
  (b) ∑y<∑
  (c) ∑y>∑      
  (d) None         
  
  
• One byte equals:
  
  (a) 8 bits         
  (b) 4 bits         
  (c) 6 bits         
  (d) 12 bits

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

2. Write short answers of any Eight Parts. 16

• Write down any two properties of Normal Distribution.
• Explain why β1 equal to zero for normal distribution.
• M.D = 16 Find the value of standard deviation.
• The value of pµ2 = 4 Find µ3 and µ4 about Mean for normal distribution.
• In a standard normal distribution what is the value of mode and median?
• What is meant by unbiasedness?Identify. the estimator and Estimate if a sample of 11 cricket players give an average score of 23.
• What is meant by Estimation?
• Explain difference between one tail test and two tail test.
• What is level of significance?
• Write the names of output devices.
• What is computer?

3. Write short answers of any Eight Parts. 16

• Differentiate between parameter and statistics.
• What is sample design?
• What is meant by probability sampling?
• Define sampling distribution.
• Differentiate between sampling error and non - sampling error.
• Define standard error.         
•  Write down the properties of r.
  If byx = -1.6 and bxy = -0.4 Find the value of r.
• Define the term BIAS.
• Differentiate between regression and correlation.
• What is meant by Scatter diagram?
• Given Sxy = 72, Sx = 4 and. Sy = 18. Find the value of ryx.

4. Write short answers of any Six Parts. 12

• Define contigency table.        
  
• Expalind the term attribute.
• If N = 1000, (A) = 400, Find (α) .
• What is meant by signal in time series?
• Give any two examples of secular trend.
• What is meant by seasonal trend?
• Define noise in time series.
• Calculate three-values moving average for 206, 209, 212, 215,
  218, 221.
• In a time series  = 80+5y. Find intercept and slope of the series.

SECTION -II

Attempt any THREE questions. Each questions carries 8 marks.
Question#5
(a) In a normal distribution the mean is 5 and variance 1. Write down its equation. Also find the value of maximum ordinate.
(b) If X N (24,16) , then find the 33rd percentile and 9th decile.

Question#6
(a) A population consists of value 10, 20 , 30 , 4o and 50. Form sampling distribution of sample mean when sample size n = 3 are drawn and sampling is done without replacement.
(b) Find mean and variance of sampling distribution formed in part (A) of the question and verify the relation.

Question#7
(a) A random sample of 75 student is selected and 16 are found to have cars on campus. Use 95% confidence interval to estimate the fraction of student who have cars on campus.
(b) The heights of college male students are known to be normally distributed with a mean of 67.39 inches and  = 1.30 inches. A random sample of 400 students showed a mean height of 67.47 inches. Using a 0.05 level of significance. Test the hypothesis Hₒ = µ = 6739 and H1= µ > 67.39 .

Question#8
(a) Regression line "Y on X" is 3X = 43 -
Regression line "X on Y" is
42Y = 2-
Identify the two regression coefficients.
(b) Compute coefficient of correlation (ruv)
u=x-25/5, v= Y-10/2

Question#9
(a) An investigation into color-blindness and sex of a person gave the following results.
Color blindness

Is there evidence at the 5% level, of significance and association between the sex of a person and whether or not they are color blind?
(b) For the following data compute 4-year centred moving avera es.

SECTION-III(Practical Part)
Note: Attempt any THREE questions.10.
(A) Take all possible samples of size 3 without replacement from a population: 1, 2, 3 , 4. Make a sampling distribution of sample variance,    and show that

(B) Take all possible samples of size 3 without replacement from apopulation: 1, 2, 3, 4. Show that sample proportion is an unbiased of the population proportion is an unbiased estimator of the population proportion.

(C) Given the data

Find estimated regression line of production on Fertilizer.
Estimate production when fertilizers is 450.

Calculate coefficient of rank correlation by pear man's tonne a.
Also comment your answer.

Find the equation of the semi-averages trend line. Compute out e trend values. Estimate the number of books sold (y) for the year 1980.