Faisalabad Board 2014
Paper Statistics Part – II
Time 20 Minutes
(Objective part)
marks : 17
Note: You have four choices for each objective type question as A, B ,C and D. The choice which you think is correct: fill that circle in front of that question number. Use marker or per to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Question#1

• The mean of standard normal distribution is:
  
  (a) 1
  (b) 0 
  (c) 100
  (d) ∞
  
  
• The normal distribution is:
  
  (a) U-shaped
  (b) J-shaped
  (c) Bell shaped
  (d) None
  
  
• Which is correct regarding normal distribution?
  
  (a) ẞ = 3
  (b) ẞ2 = 0
  (c) Q1 =μ - 0.6745σ 
  (d) None
  
  
• The mean of sampling distribution of x is:
  
  (a) μ
  (b) σ
  (c) μ  - σ
  (d)  
  
  
•   if N = 5, n = 3 for sampling with replacement then number of possible samples are:
  
  (a)  10
  (b) 125
  (c) 60
  (d) 75
  
  
• The collection of all elements under study is called:
  
  (a) Population
  (b) Sample 
  (c) Parameter
  (d) None
  
  
• if E () =then is called:
  
  (a) Biased
  (b) Consistent
  (c) Good
  (d) Unbiased
  
  
• Biase is:
  
  (a) Cumulative
  (b) Decumulative
  (c) Decreasing
  (d) None
  
  
• The probability of type - I error is denoted by:
  
  (a) a
  (b) ẞ 
  (c) 1 – a 
  (d) 1 - ẞ
  
  
• In regression,  Σ is equal to:
  
  (a) 0 
  (b) Σy
  (C) Slope 
  (d) None
  
  
• A simple linear regression model contains:
  
  (a) One variable
  (b) Two variables 
  (c) Three variables 
  (d) None
  
  
• If rxy = -0.84 then rxy is:
  
  (a) 0.84
  (b) 0.42
  (c) -0.84
  (d) None
  
  
• Association measure the strength of relationship between:
  
  (a) Variable 
  (b) Attributes 
  (c) Constants 
  (d) None
  
  
• n – (ẞ)  is equal to:
  
  (a) (A)
  (b) (B) 
  (c) (a)
  (d) (ẞ)
  
  
• For best fitted line Σ  (y - 2 is:
  
  (a) Maximum
  (b) Minimum
  (c) Zero
  (d) None
  
  
• Secular trend is a ____________ term variation.
  
  (a) Short
  (b) Fixed 
  (c) Long 
  (d) None
  
  
• Set of electronic instruments is:
  
  (a) Software
  (b) Hardware
  (c) Output
  (d) None

Section I
Time 3:10 hours
subject part
Marks 83

2.Write short answer of any eight questions.(8x2=16)

• Write down probability density function of normal distribution.
• What is relationship between quartile deviation and standard deviation of normal distribution?
• How are standard deviation and mean deviation of normal distribution related with each other?
• What are values of ẞ1 & ẞ2 for normal data? Interpret it.
• Discuss points of inflexion of normal distribution. Are they equidistant from mean?
• what is pooled estimator of variance?
• Find pooled estimator of population proportion.
• Define interval estimation.
• Define hypothesis testing, null and alternative hypothesis.
• What is t-statistic?
• Name some hardware components of a personal compiler.
• Name some software components of a personal computer.

3.Write short answer of any eight questions.(8x2=16)

• What are the limitations of sampling?
  
• Define quota sampling.
• If   μ =10 and      =  2.5. Compute the value of  = ? and σ2?
  
• How can we define bias?
  
• If n = 100 and N= 240, μ = 20, σ = 5 then find   ? and of  .?
  
• What is sampling and non-sampling error?
  
• Write a short note on scatter diagram.
  
• What are the properties of regression coefficients?
  
• Given  = 1.87, bxy = 0.25,  , = 12.45 Find a = ?
  
• Given bxy = 0.82, rxy = 0.97, Find byx = ?
• What is the difference between regression and correlation?
• Given rxy = 0.8, sx = 4, sxy = 20, find sy = ?

4. Write short answer of any six questions.  (6x2=12)

• Explain the term +ve and -ve attribute.
• Define a contingency table.
• Explain the term rank correlation.
• Given (AB) = 30, (A) = 40. Find (Aẞ).
• What is meant by analysis of time series?
• Explain seasonal variations.
• Explain the method of moving average in a time series.
• Give names of different methods of measuring secular trend.
• Write down four components of time series.

Section – II

Attempt any three questions. Each question carries 8 marks
Question#5
(a)  The mean and standard deviation of normal distribution are 100 and 20 respectively. Find area:
(i) Between 65 and 85 
(ii) Between 65 and 125
(b) Find two points having 98%, of the area between them.

Question#6
(a) Suppose a 'tandem sample of size "n" is taken from a  population of size "N". Assume n = I compute σX if sampling is done:
(i) With replacement
(ii) without replacement
(b) A small professional society has N = 4500 members. The president has mailed n = 400 questionnaires to a random sample of members asking whether they wish to affiliate with a large group. Assuming that the proportion of the entire membership favouring consolidation is p = 0.7. Find the mean and standard error of the sample proportion .

Question#7
(a) Give the following information n = 12,   = 209, 2 Find 95% confidence interval for the population mean: (μ).
(b) Given the following information: n = 16,x = 11, 2  = 81.Test the hypothesis that mean of the population is more than 10.

Question#8
(a) From the following results show that 'r' is the geometric mean of two regression coefficients:
Σ (x - x)2  = 80,  (y - Y)2  = 170, Σ (x -x )(Y - Y) = 100
(b) The correlation coefficient for a sample of 20 observation is 0.6, if X)=12, Y=20, S2 = 2. Estimate the line of regression of y on x.

Question#9
(a) Using a 5% level of significance, test whether there is any connection between the beaches and sex?

(b). fit a straight line y = a + bx and find y when x = 70:

Section – III

10. Attempts any three questions. Each question carries 5 marks.
(A) Draw all possible samples of size two from the population U, M, M, U and M. FiNd sample proportion 0) of in each sample and verify that:  
E () = P & VAR () =  ,  .
(B) A group of 5 students are found to have the following i.q’ S: 109, 112, 113, 120 & 125. Is it reasonable to suppose that these students have come from a large population whose average I.Q is 118?
(C) Estimate correlation co-efficient from the following data:

(D) Rank the value and calculate renk correlation coefficient: