Inter (Part-II Gujranwala Board 2014)
Statistics (New Scheme)
Paper : II (Objective)
Time: 20 Minutes
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 with marker or pen on the answer book provided. Cutting or tilling, two or more circles will result in zero mark iri that question. Attempt as many questionVirgh7erin objective type question paper and leave others blank.

Question#1

• In a standardized normal distribution variance is
  
  (A) 1
  (B) O
  (C) π
  (D) O²
  
  
• The coefficient of skewness of a normal distribution is
  
  (A) Zero
   (B) Positive
  (C) Negative 
  (D) Both positive and negative
  
  
• In a normal distribution, the values of β1, and β2 are respectively
  
  (A) 0 and 3
  (B) 3 and 0
  (C) 0 and 1 
   (D) I and 3
  
  
• The standard error of mean for o2 = 16, n = 4, is
  
  (A) 1
  (B) 2
  (C) 4
  (D) 8
  
  The random digit from 0 to 9 are called
  
  (A) Triple digit
  (B) Single digit
  (C) Double digit
  (D) All
  
  
• A value calculated from sample is called a
  
  (A) parameter
  (B) statistic
  (C) mean 
  (D) proportion
  
  
• For unbiasedness
  
  (A) E(ẋ) ≠µ
  (B) E(ẋ)+µ
  (C) E(ẋ)= µ 
  (D) E(ẋ)- µ
  
  
• The hypothesis which is to be tested for possible rejection is
  
  (A) Simple
  (B) Composite
  (C) Null
  (D) Alternative
  
  
• The probability of type II error is
  
  (A) α
  (B) β
  (C) 1 - α
  (D) none of these
  
  
• If y = a +bx, which one is always true.
  
  (A)(x-ẋ) = 0
  (B)∑ (x-ẋ) =∑(y-ẏ)
  (C) ∑(y-ẏ)=0
  (D) ∑(y-ẏ)2 = 0
            
• In estimated regression line ẏ = a+bx. Is called
  
  (A) Slope
  (B) Intercept
  (C) Random error
  (D) Regressor
  
  The value of r2 for a particular situation is 0.49. What is the coefficient of correlation?
  
  (A) 0.49 
  (B) 0.7
  (C) 0.07
  (D) none ,of these
  
  
• A characteristic which varies in quality from one individual to another is called
  
  (A) Variable 
  (B) Statistic
  (C) Attribute.
  (D) Regression.
  
  
• For a contingency table of order r x c the number of degree of freedom is equal to
  
  (A) rc
  (B) (r -1)c
  (C) (c-1)r 
  (D) (r-1) (c-1)
  
  
• Methods of secular trend are  CO
  
  (A) 2 
  (B) 3
  (C) 4
  (D) 5
  
  
• The difference between the actual value and trend value is called
  
  (A) Slope 
  (B) Residual
  (C) Intercept
  (D) Sum of residuals
  
  One byte =________
  
  (A) 4 bits
  (B) 6 bits
  (C) 8 bits
  (D) 16 bits

Inter (Part-II)
Gujranwala Board 2014
Statistics (New Scheme)
Paper II (Subjective)
Time: 3:10 hours
Marks: 83
Note: Section 1 is compulsory. Attempt any three (3) questions from Section II and any three parts from Section III.
(SECTION-I)

2. Write short answers to any EIGHT questions: (2x8=16)

• What is meant by normal curve?
  
• How many parameters normal distribution has?
  
• Write down any two properties of the normal distribution,
  
• What is the role of “o” in normal distribution?
  
• If  x -N N (24, 16), find Q1 and Q3
  
• What is meant by statistical inference?
  
• What is meant by point estimate?
  
• Define the term alternative hypothesis.
  
• What is meant by type-I error?
  
• What is meant by one-tailed test?
  
• What is meant by the term computer?
  
• Write down the main categories of computers.

3. Write short answers to any EIGHT questions. (2x8=16)

• What do you know about sampling design?
  
• What are sampling units and sampling frame?
  
• What are two main types of sampling design?
  
• Discuss random sampling with replacement.
  
• Discuss random sampling without replacement.
  
• Give some methods of selection of simple random sampling,
  
• What is sum of residuals?
  
• What is sum of squared residuals?
  
• Name the point through which each regression line passes.
  
• Write down formulae of byx in different forms.
  
• Write down formulase of a in various forms 
  
• If U =   and V =  Is b_yx = b_vu ? Yes or No? Why? Comment.

4. Write short answers to any SIX questions: (2x6 = 12)

• Differentiate between attribute and variable.
  
• What is positive association?
  
• Define co-efficient of association.
  
• What is the difference between signal and noise?
  
• What do you mean by secular trend?
  
• Give some examples of irregular variation.
  
• Define analysis of time series.
  
• Give two de-merits of free hand curve.
  
• Define principle of least square.

(SECTION-II)

Question#5
(a) In a normal distribution, M.D = 3.9895. Find standard deviation., quartile deviation, second and fourth . mean moment to the normal distribution. 4
(b) X is a normal variate with mean 1 and standard deviation 3.Find the probability that 3.43 ≤ x ≤ 6.19. 4

Question#6
(a) Take all possible samples of size 2 with replacement from the population 1,3 ,5. Show that. 4
(b) If n = 25 and var( x )=.0.25, what will be the value of n if oar ( x ) is increased to 1.25? 4

Question#7
(a) A random sample of 16 values from a normal population showed a mean 41.5 inches and a sum of the squares of deviations from this mean equals 135 (inches)2, Show that 95% confidence limits for mean are 39.9 and 43.3. 4
(b) A coin is tossed 400 times and head appeared 216 times. Test the hypothesis that coin is fair at 1% level of significance.

Question#8
(a) Compute the regression coefficients ∑(x— x )(y  - y) = 148 . 4
Sx = 7.933 Sy =16.627, n = 15
(b) Find correlation coefficient of part (a) and show that correlation coefficient is the geometric mean of two regression coefficients. 4

Question#9
(a) N = 100, (A) = 40 (B) = 60  (AB) = 20. Find coefficient of association (Q). (b) Given y= 1,2,3,3,6. 4
x = 0,1,2,3,4 and ẏ=0.6+1.2 x, compute ∑ e,

(SECTION-Ill)
(Practical)

Question#10
(a) A population consists of values 0, 3. 6 and 9. Take all possible simple random samples of size ‘3' without replacement. Form the sampling distribution. of sample mean ẋ. Hence state and verify the relationship between
(i) The mean of ẋ and the population mean.
(ii) The variance of ẋ - and the population variance.
(iii) The standard error of ẋ and the population standard deviation
(B) Given that
x₁75, n₁ = 9 ,∑(x_i1 — ẋ₁)² =1482
x₂ = 60, n₂ =16 ,∑(x_i2 —x₂)² =1830 -
Assuming that the two samples were randomly selected from two normal populations in which σ12 = σ12 (but unknown),-calculate an 80% confidence interval for the differentiate between the two population means
(C) The following data were obtained for a sample of 10 men From a height and weight distribution. 5
x=70, Y = 155 ∑( x₁- x)2 =120
∑y², = 240550, ∑(x₁- x)(y, —y)= 150
Calculate covariance, correlation coefficient and two regression lines. 
(D)Discuss the resemblances of stature of parents and off- springs for the following data

(e) The following table show the property damaged by Road accidents in Punjab for the year 1973 to1979.

• Obtain the semi-averages trend line.
• Find out the trend values