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FAISALABAD BOARD 2013
PAPER STATISTICS
PART-II
Time: 20 Minutes
(Objective Part)
Marks: 17
Note: Four Answers are given against each column A, B, C & D. Select the write answer and only separet answer sheet, fill the circle A, B, C or D with pen or marker in front of that question number.

Question#1

Is the probability associated with:

(a) Level of confidence
(b) Level of significance
(c) Type-I error
(d) None
The end points of a confidence Interval are called:

(a) Population limits
(b) Confidence limits
(c) Sigma limits
(d) None
Y = a + bx + e then slope is:

(a) B
(b) X
(c) A
(d) Y
The range of correlation coefficient is:

(a) 0 to 1
(b) -1 to +1
(c) 1
(d) None
The relationship between two variables is:

(a) Regressand
(b) Regression
(e) Correlation
(d) None
Presence of attributes is denoted by:
(a) Small letters
(b) Capital fetters
(c) Greek letters
(d) None
The range of chi square distribution is:

(a) 0 to
(b) -∞to ∞
(c) 0 to 1
(d) None
The time series has components:

(a) 6
(b) 5
(c) 4
(d) None
The removal of any component of time series is called:

(a) Decomposition
(b) Detrending
(c) Randomization
(d) None
All the arithmetic operation in a CPU are carried out:

(a) ROM
(b) ALU
(c) RAM
(d) None
In normal distribution µ = 50 and - σ =7, if y = x -7, then S.D. of y is:

(a) Zero
(b) 14
(c) 7
(d) 49

In a normal distribution µ ± 0.6745 covers an area equal to:

(a) 50%
(b) 68.27%
(c) 95.45%
(d) 99.73%

If X~N (100, 64) then µ2 will be:

(a) 164
(b) 64
(c) 100
(d) None

The difference between E (x) - µ is called:

(a) Sampling error
(b) No error
(c) Biased
(d) None

If x= 10 and µ = 12 then sampling error is:
(a) 10
03) 2
(c) 12
(d) None

A survey conducted by a sample designs is called:

(a) Sample survey
(b) Population survey
(c) Biased survey
(d) None

The kinds of estimation are:

(a) 3
(b) 2
(c) 4
(d) None

Time: 2:40 Hours
(Subjective Part)
Marks: 68
SECTION - I
2. Write short answers of any Eight Parts.16

Define normal frequency distribution.

Write down the equation of the standard normal distribution.

The mean deviation of a normal distribution is 16. Find the value of its standard deviation.

Define the points of inflections in normal distribution.

Write down any four properties of normal distribution.

Define test-statistic.

Define level of significance

Differentiate between simple and composite hypothesis.

Given 120, µo = 100, s = 34.75 and n = 25. Find t.

Write down the different type of computers.

What is meant by programming?

Define estimation and write the names of its different types.

3. Write short answers of any Eight Parts. 16

Explain the term sampling frame.

What is simple random sampling?

How many samples can be selected without replacement when N = 5 and n = 4?

What is when N= 10, n = 2 and σ= 9 and samples are selected without replacement?

Define sampling distribution of proportions.

What are non-sampling errors?

Given ∑(x - x)(y-y) = 100, n 10 and S_x = 6 Find byx.

Give two formulas for calculating r.

What is causation?

Given Sxy = 128 and bxy = 2 Find the value of Sy

What is regression?

Give any two properties of r.

4. Write short answers of any Six Parts. 12

Distinguish between attribute and variable.

Define contingency table.

Write the direct formula of, x² in 2 x 2 contingency table.

Define secular trend.

Distinguish between signal and noise.

What do you know about principle of least square?

Define seasonal variations.

Define irregular variations.

Give the equation of parabolic curve of 2nd. order.

SECTION-II:

Attempt any THREE questions. Each questions carries 8 marks.
Question#5
(a) In a normal distribution the lower and upper quartiles are respectively 8 & 17. Find the parameters of the normal distribution. 4
(b) Past experience shows that 9% of the electricity bills are deposited with delay. If 20000 bills have been dispatched, find the probability that the number of bills with delay is:
(i) At least 1750
(ii) Less than 1750

Question#6
(a) Draw all possible samples of size 2 w.r. from the population 2, 4, Find mean of means and of variances. Discuss the results.4
(b) S.E. of sample means of 100 is 2. What would be the value of S.E. of sample means if sample size is reduced to 50? 4

Question#7
(a) Five young recruits were put through a physical training program. The weights were recorded as

Weight before (kg)
40

37

38

42

43

Weight after (kg)

42

36

40

42

45

Find 95% confidence interval, assuming the weights are normally distributed. 4
(b) A sample of size 56 from a normal population with unknown variance 2 with mean 40 and variance 950. Test : µ = 45; : µ ˂ 45 Let α = 10. 4

Question#8
(a) Compute the regression coefficients in the following case: n = 10 ∑ (x-x)² = 170 ∑(y-y)² =140 ∑ (x -x) (y-y) =92
(b) Compute the coefficient of correlation from the given data: 4
X: 21, 22, 23, 24, 25
Y: 25, 24, 23, 22, 26

Question#9
(a) Compute rank correlation coefficient from the following data of students marks: 4

Students
A

B

C

D

E

F

G

Marks in Eco

15

22

60

25

50

40

42

Marks in Math

30

25

50

35

55

45

40

(b) Fit trend line from the following time series and compute trend values: 4

Years
2005

2006

2007

2008

2009

2010

2011

Value

21

24

23

26

25

28

27

Students	A	B	C	D	E	F	G
Marks in Eco	15	22	60	25	50	40	42
Marks in Math	30	25	50	35	55	45	40

Years	2005	2006	2007	2008	2009	2010	2011
Value	21	24	23	26	25	28	27