Multan Board 2016
Paper stat
(Session: 2016)
(Group- II/ A- 2012)
Class – 2nd  Year 
Paper – II
Time: 20 Minutes 
(OBJECTIVE) 
Marks: 17 
Note:    Four answer are given against each question in columns A,B,Cor D with pen or marker in front of that question number.

• If n = 8, =120,= 302 then unbiased estimates of the population variance is
  
  (A) 15
  (B)  43.14
  (C) 37.75
  (D) 120
  
  
• An error is made by accepting H0 if H1 is actually true:-
  
  (A) Type II error
  (B) Type I error
  (C) Sampling error
  (D) None of these
  
  
• Level of significance is denoted by:-
  
  (A)
  (B) 1 –
  (C)  a
  (D) 1-
  
  
• Regression co-efficient is independent of:-
  
  (A) Scale
  (B) Orison
  (C) Both A and B
  (D) None of these
  
  
• A correlation co-efficient lies between:-
  
  (A) - 1 to 0
  (B)  0 to I
  (C)  - 1 to + 1
  (D)  + 
  
  
• If b_y.x= 0.16, b_x.y = 0.04 then rxy is:-
  
  (A) 0.08
  (B) 0.8
  (C) 0.16
  (D) 0.04
  
  
• For (4 x 5 ) contingency table the no of cells is equal to:-
  
  (A) 4
  (B)  15
  (C) 20
  (D)  16
  
  
• In a chi-square test for independence no expected frequency should be______ than 5.
  
  (A) Greater
  (B) Less
  (C) Both A and B
  (D) None of these
  
  
• The graph of time series is called:-
  
  (A) Historigrarn
  (B)  Scatter Diagram
  (C)  Frequency Curve
  (D)  Histogram
  
  
• The best fitting trend is one in which the sum of squares of residuals is:-
  
  (A) Maximum
  (B) Zero
  (C) Least
  (D) Negative
  
  
• A decimal number system has base:-
  
  (A) 8
  (B) 10
  (C) 2
  (D) 16
  
  
• The normal distribution is a:-
  
  (A) Unimodel
  (B) Multimodel
  (C) Bimodel
  (D) Tri-model
  
  
• In a normal distribution -0.6745 or is equal to:-
  
  (A) 3
  (B)
  (C)
  (D) 1
  
  
• For the standardized normal viarate P=
  
  (A) 1
  (B) 0
  (C) 0.5
  (D) 0.75
  
  
• A population consists of 5 members 1, 2, 3, 4, 5 then proportion of even numbers is:-
  
  (A)
  (B)
  (C)
  (D)
  
  
• A value calculated from population is called:-
  
  (A) Parameter
  (B) Statistic
  (C) Population
  (D) Sample
  
  
• If  = 22 and = 20 then sampling error is equal to:-
  
  (A) 2
  (B) 20
  (C) 22
  (D) 42

INTERMEDIATE PART-2
Section 2

2. Attempt any eight parts.

• In a normal distribution s = 243 find parameter
•  What are the mean and variance ofNormal Distribution?
•  Find the value of maximum ordinate for normal distribution, when = 25 and  =25
•  What arc the parameters of Normal Distribution?
•  Whet are the Q . D and M.D of the Normal Distribution?
•  Given  =120, 0 100, S= 34.75 and n= 25 find t.
•  Define Level of Confidence.
• Define Statistical Inference.
•  Define type II-error.
•  Define Simple Hypothesis.
•  What do you know DOS?
•  In Computer Studies, what do you understand by Binary Number System?

3. Attempt any eight parts.

• Define Sampling Frame.
•  Elaborate the term Statistic.
•  Explain Probability Sampling.
•  What do you understand by Standard Error?
•  In a population with  = 50 and = 250. Find the mean and variance for the sampling distribution of mean if sampling is done with replacement with n = 50.
• Given  = 40,  =4. S.E () = 2. Find n.
•  What is meant by regression co-efficient?
•  Write down two properties of slope.
•  Define simple linear regression co-efficient.
•  Explain the term negative correlation.
•  Interpret the mean of r =1
•  Given  =1.  = 8, b= 2. Find the value of intercept 'a'.

 4. Attempt any six parts.

• Explain the term rank correlation
•  What is meant by independence of attributes? Explain
•  Given the pairs of ranks (4. 2), (I, 3), (2, IL (5, 6), (6, 5), (3, 4). Find .
•  Define Time Series.
•  Explain the term Secular Trend.
•  Given (y —) = 0.5, -0.5, 1,-1, 0.5, - 0.5. Find sum of squares of residuals.
•  In a time series Y = 16 + 0.2x. Determine Y - intercept and slope of the line.
•  Write down additive model of time series.
•  What are the different components of a time series?

 Note: attempt any three question                                                
Question#5
(a) XN(50,) and P(x<69.9)=0.993 find the value of a.
(b) if XN (24,16) find
(i) P₂₀
(ii) D₉
Question#6
(a) what will be the mean and variance of sample means if a sample of 36 is draw with replacement from the population 1,2,3,4,4,4,5,6,6,7.
(b) Given P₁ =,P₂ =,n₁ =2, n₂ =2 sampling is done with replacement.
(i) E(₁-₂ )
(ii) S.E(₁-₂ )
Question#7
(a) In a sample of 500 items. 40 are defective.  Compute 95%  confidence  interval for the proportion of defective in the population.
(b) A class of six students was given a test before coaching and after one month coaching their marks were as follows:- 

Test the hypothesis that coaching on the averages has improved the performance of students.
Use =5%
Question#8
(a) The following table shows the marks obtained by students in Economics(X) and Statistics  (Y).

Find the least squares regression line y on x and show that =
(b) Compute co-efficient of correlation by finding missing value when  = 6  = 8 for the data given below.

Question#9
(a) Test H0: the two attributes are independent if 470 passed out of 750 append students. 465 had attended classes and 58 of them failed.
(b)  Suppose  = 50 + 2x with origin at 1983 and unit of measurement for x is one year. Shift the origin at 1980.

SECTION-III (PRACTICAL)
NOTE: - Attempt any three parts

(D) Compute co efficient of rank correlation from the following ranks.

(E) Compute 4 years centered moving average from the following time series.