Inter (Part-II) Bahawalpur Board 2015
Statistics
Part II (Objective Type)
Time Allowed: 20 Minutes 
Max. 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 pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• In a Standard Normal Distribution Variance is:

(A) 0
(B) 1
(C) α²
(D) π

• In a Normal Curve µ ± • 6745 α includes:

(A) 50% Area
(B) 68 • 27 Area
(C) 95 • 45 Area
(D) 99 •73 % Area

• In a Normal Distribution µ3 is always

(A) 0
(B) < 0
(C) > 0
(D) 3

• Population Parameters are denoted by:

(A) Roman Letters
(B) Greek Letters
(C) Latin Letters
(D) Englih Letters

• The complete list of Sampling Units is called

(A) Sampling Frame
(B) Sampling Design
(C) Target Population
(D) None of these

• In Sampling with replacement, a Sampling Unit can be selected 

(A) Only Once
(B) More than once
(C) Less than once
(D) None of these

• Test Statistic t = ẍ - µ /S / √n has d. f. equal to:

(A) n
(B) n - 1
(C) n - 2
(D) nl+ n2 - 2

• If E(ɵ) = ɵ , then ɵ is

(A) Biased Estimator
(B) Unbiased Estimator
(C) Positively Biased
(D) None of these

• The probability of rejecting a tree Null Hypothesis is denoted by:

(A) α
(B) Type I Error
(C) ß
(D) Type II

• Another name of Independent Variable is:

(A) Regressand
(B) Predictand
(C) Regressor
(D) None of these

• In Regression, the sum of errors i-e Σ(y - Y ) is:

(A) 0
(B) <0
(C) > 0
(D) #0

• If the two variable are uncorrelated the value of Ճ is :

(A) -1 
(B) 0
(C) +1
(D) None of these

• The strength of relation between attributes is called:

(A) Association
(B) Correlation
(C) Regression
(D) None of these

• The value of Ճ² can not be :

(A) Zero
(B) Negative
(C) Positive
(D) None of these

• In fitting Straight Line to the Time Series, sum of residuals is

(A) Least
(B) 0
(C) Most
(D) Positive

• In Semi Average Method, we divide the data into :

(A) Two Parts
(B) More than two parts
(C) Three Parts
(D) Less than Parts

• Which one of these is not an output device:

(A) Monitor
(B) Scanner
(C) Printer
(D) Modem

Inter (Part-II) Bahawalpur Board 2015
Statistics
Part II(Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Section I

Q.2. Attempt any eight parts.

• Write down the Probability Density Function of the Normal Curve.
• Write down any two properties of the Normal Distribution.
• What is the role of (α)- in Normal Distribution?
• If x ,..., N ( 15.4 ). Find the value of Z if x= 18
• In a Normal Distribution, Q₁ = 8, Q₃= 17. Find Mean and Standard Deviation.
• What is meant by Statistical Inference?
• What is mutt by Point Estimate?
• Define the term Alternative Hypothesis.
• What is meant by Simple Hypothesis?
• What is meant by Two Tailed Test?
• Differentiate between Hardware and Software
• What is Computer?

Q.3. Attempt any eight parts.  

• Define Sample.
• Explain Finite Population.
• What do you understand by Statistics?
• Explain the term Sampling Error.
• For a Population µ = 30, α= 5 , n = 100 find Hẍ and α²/x
• Given P1 = 2/3, P2 = 1/2 , n₁ =2, n2 = 2 Find p₁-p₂ and E (P₁ – P₂)
• Elaborate Residual
• Describe Regression Coefficient
• Explain Positive Correlation.
• Write down two properties of Regression Line.
• Given x = 1 , y= 8 and b = 2 find the value of intercept a
• Given S_xy = 16 and S_xS_y = 81 , find r –

Q.4. Attempt any six parts.    

• Define a Contingency Table.
• What do you understand by Association?
• Explain the term Rank Correlation
• Define Cyclical Movements
• What is meant by Seasonal Variation?
• Define Forecasting in the Time Series.
• Explain the method of Least Square in a Time Series.
• Given Ẏ = 128 + 4x and x = - 3 , - 2 ,- 1, 0,1, 2, 3 find ΣẎ .
• Define Additive Model of a Time Series

Section-II

Question #5
(a) In a Normal Distribution µ = 40 and P(25 < x <55) = • 8662 , find P [ 20 < x < 60]. (4)
(b) Suppose that x is normally distributed with µ = 25 and α= 5. Find the Lower and Upper Quartile. (4)

Question #6
(a) Given the information n₁ = 49, µ₁ = 6 • 5 , α_1-0.9, n₂ = 64, µ₂ = 6, α₂ = 0.8 Find the Mean and Variance of Sampling Distribution of Difference. (ẍ₁ - ẍ ₂ ). (4)
(b) Find the Population Mean and Variance if samples of size 2 with replacement. Given Mean and Variance as 10 and 2 • 5 respectively. (4)

Question #7
(a) A random sample of 8 acres was selected from a particular variety of wheat Make 99% C.j. for average production of wheat from the given data. Production 52 , 41 , 68 , 72 , 63 , 37 , 51 and 55. (4)
(b) A machine puts out 16 imperfect articles in a sample of 500. After the machine is over hauled, it puts out 10 imperfect articles in a sample of 300. Has the machine out put improved after overhauling at α = 0.05 ? (4)

Question #8
(a) Estimate the linear regression of y on x for the following data. (4)

Also estimate y for x = 600
(b) The two regression coefficients have the following values. Find r. (4)
(i) b_yx = 0.86, b_xy = 0 • 95
(ii) byx = - 0 • 52 , b_xy = -1.02

Question #9
(a) 750 students appeared in an examination and 470 were successful. 465 had attended classes and 58 of them failed. Calculate the coefficient of association to discuss association between attending classes and success.
(b) Why the method of least squares derive a linear trend to the following results for the years 1985 to 1994 (both inclusive):- Σx .0, ΣY = 322 , ΣXY =1550, Σx2.330. Find out trend values as well.

Attempt any three Parts Section-III ( Practical Part )

Question #10

(a) If x~ N (µ; α²), p(x<40) = 0.1587 , P( x> 70) = 0 • 0228 then find " µ and α ". (5)

(b) Given that (i) n₁ = 100, ẍ₁= 2100, α₁ = 224 (5) (ii) n₂ = 110, ẍ₂= 2100, α₂ = 192 Compute 95 % Confidence Interval for (µ _l - µ ₂)

(c) Compute Coefficient of Correlation between Dx and Dy from the following (5) data. Dx = x - 100 , Dy = y - 90

(d) Test the Hypothesis that there is no association between Intelligence of (5) fathers and sons. Use α= 5%

(e) Compute Trend Values by the method of Semi Average. (5)