Sargodha board 2015
(Statistics)
(Inter part2)
(OBJECTIVE)
Note:Pour possible answers A, B; C and D to each question are given. The choice which you think is correct that circle in front that question with Marker or Pen ink.'Lining or filling two or more circles 'will result in zero mat k in that question. Write the letter A, B. C or D in the column.(write correct "option) against each question also. If there k a contradiction in the bubble and hand written answer, bubble option will be considered correct.

• In normal distribution µ=12 σ² = 25 the 1^st mean moment is
  
  (A) 2
  (B) 0
  (C) 4
  (D) 8
  
  
• The maximum ordinate of normal curve is at
  
  (A) x = µ
  (B) x = σ²  
  (C) x = x
  (D) x = s²

• The Q.D for standard normal distribution is.
  
  (A) 0.6745
  (B).69
  (C).77
  (D).99
  
  
• The no. of all possible samples in sampling with replacement is
  
  (A) N_n
  (B) Nⁿ
  (C) N³
  (D) N²
  
  
• The sampling error is
  
  (A) x - µ
  (B) µ x 2
  (C) x - µ
  (D) µ + 3
  
  
• If E(P)=3/5  the value of population proportion is.
  
  (A) 5/3
  (B) 2/5
  (C) 3/5
  (D) 4/6
  
  

• The Level of significance is denoted by
  
  (A) β
  (B) ∝
  (C) >
  (D) θ
  
  
• A value of abrtstimator is called
  
  (A) Constant
  (B) Formula
  (C) Estimate
  (D) Population
  
  
• The alternative Hypothesis is denoted by
  
  (A) H1
  (B) H0
  (C) H3
  (D) H4
  
  
• If bxy is -Ve then byx will be
  
  (A) +
  (B) -
  (C) 0
  (D) 1
  
  
• If correlation co-eff xyx=0.48 then xyx will be
  
  (A).84
  (B).44
  (C).48
  (D).88

• If both regression Co-efficient are -Ve then the corr. Co-eff. Is
  
  (A)+ve
  (B)-ve
  (C)2
  (D)3
  
  
• The value of x² test in always
  
  (A) 0
  (B) +ve
  (C) -ve
  (D) 1
  
  
• If [(6∑d²)/(n(n²-1))]= 0 then r, will be
  
  (A) 1
  (B) 2
  (C) 0
  (D) 4
  
  
• In fitting a line the value slope remain same by change of
  
  (A)Scale
  (B)Origin
  (C)Both
  (D)None

• The best-fined trend is one in which the sun, of squares of error is
  
  (A)-ve
  (B)+ve
  (C)0
  (D)Minimum
  
  
• The diameter of compact clink is
  
  (A)4.75
  (B)4.15
  (C)5.52
  (D)3.77

SUBJECTIVE PART
Inter part2
SECTION I

Question#2
Write short answer of any eight parts.

• Write down any two properties of Normal Distribution.
• The M.D of a Normal Distribution is 16. Find the approximate value of variance.
• What is Standard Normal variate.
• Write the lower and upper quartile of Normal Distribution.
• Define the Point of Inflection
• Define type 1-error with example.
• What is unbiased estimator?
• Differentiate b/w simple hypothesis and composite hypothesis.
• Define degree of freedom
• Define confidence Interval
• Differentiate b/w Hardware and Software
• What are the output devices in the computer.

Question#3
Write short answer of any eight parts.

• Differentiate between finite and infinite population
• Given. µ = 6, n = 2, σ² = 10.8 Find E(S²)
• What is the value of finite Population Correction factor when n=18 and N=425.
• Draw all possible Samples of size 3 without replacement from the population 2,4,6,8,9.
• Explain the term sampling frame.
• Describe the properties of the sampling distribution of sample mean.
• What is meant by regression?
• What is meant by residua?
• Define the Principle of least square.
• Write down any two properties of correlation coefficient.
• If b_n= 1.4 and r_n = 0.87 find b_n.
• Write a short note on Scatter diagram.

Question#4
Write short answer of any six parts.

• Define association of attributes
• Define positive and Hagar ye association.
• What is contingency table
• Define time series.
• What are the main components of time series.
• Define Historigram.
• What is multiplicative model in a time series?
• What are the four phases of business cycle?
• Define secular trend.

SECTION II
Note: Attempt any three questions. Each question carries equal marks,

Question#5:

      (A) If x ∼ N(16, 5) Find P( between 11 & 21),
      (B) Given that µ=.300 and δ ²=100. Find Q₁ and Q₃ of the normal distribution.

Question#6:

       (A) A population consist of values 3,6 find all possible samples of size 3 with replacement and compute the mean, of each sample. Make the sampling distribution of sample means.
       
       (B) Find mean and variance of sampling distribution formed in part (a) arid verify it by suitable relation

Question#7:

       (A) Given the following information n=8, ∑x = 261.1, ∑(x-x)² = 3.22 find 90% confidence interval for the population mean (µ)
       (B) Given the following information: n=100,x = 4.35, σ 0.18 test the hypothesis that µ < 4.40 at d=0.01

Question#8:

        (A) Given y=0.84x + 10.24, x =0.36+0.62y Find value of x and y.
        (B) Compute end interpret the coefficient of correlation x: 11, 12, 14,15,16 y, 16,18, 10,20,12 (3+1)

Question#9:

          (A) Fit a straight line y=a+bx from the following result for the year 1948-1958(both inclusive). ∑x=0, ∑y=438, ∑x² = 110 and ∑xy = 84.4
          (B) The data given below shows likings of three colour pink, white and blue in a sample of 200 males and females

Test whether there is any relation between Sex and colour. Use α =0.05

SECTION III (Practical)
 Note: Attempt any three parts from the following.

Question#10:
(A) In a large restaurant, one in four customers asks for iced water with meal. Use normal distribution in calculate the probability Mai of the first 100 customers fewer Man 20 will Usk for iced water with their meal.
(B) It is claimed 90% persons cannot tell the difference between margarine and Butter, but of a random sample of 500 persons. 72 could differentiate between them. Is claimed justified at a=00.5
(C)

• n=11 ∑x=7040∑y=4235
• n∑x²-(∑x)²=168110000
• n∑y²-(∑y)²=8910000
• n∑xy-∑x∑y=9245500

Use the least square method to fond two regression lines.
(D) For the data given below determine whether the two attributes are independent, Positively associated or negatively associated.

• N=1024, (A)=2144 , (B)=384 .(AB)1-54
• N-1000, (A)=400 , (AB)-2200 (αβ )=50
• (AB)=70 (aβ )=10, (α B)= 30 (αβ ) =140

(E) Fit a straight line y=a+bx to the following data taking 1988-0