Inter (Part-II) Dera Ghazi Khan 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.

• The variance of the standard normal distribution is

(A) Q 
(B) 1
(C) ά²
(D) None of these

• The area between µ±0.6745 ά of a normal distribution is

(A)1.0 
(B) 2.0
(C) 0.5
(D) None of these

• In a normal distribution the respective values of ß₁ and ß₂ are

(A) o and 3
(B) 3 and 1
(C) 0.5 and 1
(D) 3 and 3

• If E(ẍ)=µ, then bias is

(A) Positive
(B) Negative
(C) zero
(D) 100 %

• The standard deviation of any sampling distribution is called

(A) Sampling error
(B) non-sampling error
(C) bias
(D) Standard error

• Any calculation on the sample data is called

(A) Parameter
(B) Statistic
(C) ẍ
(D) error

• A formula or rule used for estimating the parameter is called

(A) Estimation
(B) Estimate
(C) Estimator
(D) Point estimate

• (1-ά) is called

(A) Critical value
(B) Level of significance
(C) Level of confidence
(D) Interval estimate

• The probability associated with committing type-I errors is

(A) ß
(B) ά
(C) 1- ß
(D) 1- ά

• In simple regression equation, the number of variables involved are

(A) 0
(B) 1
(C) 2
(D) 3

• The regression equation always passes through

(A) (x, Y)
(B) (a, b)
(C) (ẍ, y)
(D) (ẍ, y)

• If both variables x and y moves in same direction, then the coefficient of correlation will be

(A) Positive
(B) Negative
(C) Zero
(D) One

• For 3x3 contingency table, the number of degrees of freedom is

(A) 3
(B) 6
(C) 9 
(D) 4

• If (AB) = (A)(B) / n, then two attributes A and B are

(A) Independent 
(B) Dependent
(C) Correlated
(D) Quantitative

• The unsystematic sequence of variations is called

(A) Noise
(B) Signal
(C) Linear
(D) Non-linear

• A business cycle has

(A) One-stage
(B) Two stages
(C) Three stages
(D) Four stages

• A binary digit is commonly called

(A) bit
(B) byte
(C) kilobyte 
(D) gigabyte

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

Section I

Q2: Write short answers of any eight questions of the following. (16)

• In normal distribution the mean and S.D are 25 and 5 respectively. Find M.D and Q.D
• The S.D of normal distribution is 4. Find its first four moments about mean
• Write any two properties of nonnal distribution
• What is the relation between binormial and normal distribution
• Write down the equation of standard normal distribution and value of its maximum Ordinate correct to two decimal places
• Define statistical inference
• What is meant by point estimation?
• Define an unbiased estimator
• Define a statistical Hypothesis
• Give ẍ=120, µ_o=100, S=34.75, n=25 find the value of it.
• Define the term program
• Distinguish between hardware and software

Q3 Write short answers of any eight questions of the following. (16)

• What is meant by population?
• Define sampling error
• Elaborate the sampling with replacement
• Express the simple random sample
• Given n=5 , P=0.5 Find άp²
• Given µ = 40, ά = 4 and άx=2, Find n
• Express the term regression
• Define regression co-efficient
• Write down four properties of correlation co-efficient
• Elaborate negative correlation
• If b_yx=1.6 and b_{xy =}  0.4 find y_xy
• Given Σ(x-ẍ)(y-y) = 100, n = 5, S²₈ = 7.2 Compute b_yx

Q4 Write short answers of any six questions of the following (12)

• Define coefficient of association
• Given (A)=34000, (B)=6000, (AB)=5300, n=70000, whether attributes are independent
• Define Chi Square statistic
• What do you mean by decomposition of time series
• Define signal and noice
• What are moving averages?
• Define irregular movement
• What is meant by residual?
• Give normal equations of second degree parabola

SECTION-II

Note: Attempt any Three questions from this section: 8 x 3 24

Question #5
(a) Let X~N (20,25), find the area under the normal curve below 30. (4)
(b) In a normal distribution µ=30 and ά=5, find a point that has 15 % area below it. (4)

Question #6
(a) Draw all possible samples of size “3” without replacement from the population "0, 6, 6, 9, 9”. and show that µẍ = µ. (4)
(b) From the question given above in 6(a) compute variance of sampling distribution of sample means and compare it with population variance. (4)

Question #7
(a) A hypothesis is tested that the mear of the population is 400 against the alternative that it is greater than 4.00. A random sample of 32 gave x = 410 and S.D = 20. Test the hypothesis at 5 % level of significance. (4)
(b) The concentration in mg/litre of an element in seven randomly selected samples are 232.5, 233.9, 234.2, 236.6, 237.3, 236.7, 240.8. Find point estimate of the population mean and population variance. (4)

Question #8
(a) The equation of two regression line Y on X and X on Y are respectively
Y= 0.84 X + 10.24
X= 0.62 Y + 0.36
Find X and Y and coefficient of correlation (4)
(b) Suppose that a shoe manufacturer takes a sample of his production in order to examine relationship between wearing performance and cost

Compute the regression line Yon X (4)

Question #9
(a) The following table shows the marks of 6 candidates in two subjects (4)

Calculate the co-efficient of rank correlation
(b) Fit a quadratic trend from the following results, for the years 1985-95 (4)
Σx=Σx³=0, Σx² = 110, Σx² =1958, Σy = 410, Σxy = 601, Σx²y = 4587, n = 11 

SECTION-III (PRACTICAL)

Question #10

Attempt any three parts from A, B, C, D and E 5x3=15

• Take All possible samples of size two from population 1, 2, 3, 4 and 5 by using Sampling without replacement. Find proportion of odd numbers in each sample. Show that µp=P and ά²p = Pq/n N-n/N-1. (5)

(B) A group of 5 students are found to have the following I, Q, S 109, 112, 113, 120 and 125, is it reasonable to suppose that these students have come from a large population whose average I, Q, S is 118. (5)

(C) Find the correlation coefficier t for the following data. (5)

(D) Find the value of x² from the following data