Inter (Part-II) Gujranwala Board 2012
Statistics
Paper: II
Time: 20 Minutes
Marks: 17
OBJECTIVE

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 filling two or more circles will result in zero mark in the question Attempt as many questions as a given type question paper and leave others blank. Write the letter A, B, C or D in  the column (write correct option) against each question. If there is a contradiction in the bubble and hand written answer, bubble option will be considered correct.

1.

• 1, The term regression was used by:
  

(A) Newton           
(B) Pearson
(C) Gallon           
(D) Spearman

• 2.    A numerical characteristic calculated from sample is
  called:
  

(A) sampling unit    
(13) parameter
(C) statistic        
(D) sampling frame

• In a standardized normal distribution variance is:

(A)1                  
(B) 0
(C) π                
(D) σ2

• Level of significance is denoted by:
  

(A) β                 
(3) 1 - α
(C) 1- β                           
(D) α

• Co-efficient of correlation always lies between:
  

(A) -1 and 0         
(B) 0 and +1
(C) 1 and 2          
(D) -1 and +1

• If N = 6, n = 3 in the simple random sample without
  replacement, how many possible sample are there?
  

(A) 20               
(B) 60
(C) 216            
(D) 36

• The range of the normal distribution is:
  

(A) 0 to ∞         
(B) -∞ to ∞
(C) 0 to n           
(D) ∞ to 0

• A specific value calculated by using the sample data
  is called:
  

(A) estimation      
(B) estimator
(C) estimate        
(D) bias

• In a sampling without replacement a sample unit may
  be:
  

(A) fixed           
(B) not-repeated
(C) repeated        
(D) none

• The shape of the normal distribution is:
  

(A) leptokurtic       
(B) platykurtic
(C) skewed           
(D) mesokurtic

• An estimator  is called unbiased if E (0) -0 is:
  

(A) >0                
(B)< 0
(C) = 0                 
(D) = I

• If two variables arc uncorrelated, they the value of the
  co-efficient of correlation is:
  

(A) -1                  
(B) +1
(C) 0                    
(D) +2  

• Brain of the computer system is called:
  

(A) C.P.U.            
(B) main memory
(C) hard disk        
(D) monitor

• The graph of the time series is called:
  

(A) histogram         
(B) scatter diagram
(C) historigram       
(D) ogive

• A characteristic which varies in quality from one
  individual to t another is called:
  

(A) Attribute              
(B) variable
(C) statistic               
(D) parameter

• Increase in use of mobile phones in Pakistan is an
  example of:
  

(A) secular trend     
(B) seasonal variation
(C) cyclical movement
(D) irregular variation

• For two independent attributes Q =
  

(A) +I               
(B) zero
(C) -1               
(D) 1 and +1

Inter (Part-II)
Gujranwala Board 2012
Statistics
 Paper: II
Time: 2.40 Hours
Marks: 68
SUBJECTIVE

Note: Section 1 is compulsory. Attempt any three (3) questions from Section II.

(Section - I)

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

• What are the parameters of normal distribution?
  
• In a normal distribution Q1 65, Q3 = 75. find µ.
  
• Why β, is zero in a normal distribution?
  
• The Q.D. = 3.3725 in a normal distribution. Find the
  value of mean deviation.
  
• Find the equation of a normal distribution with mean=
  µ and variance = σ2.
  
• What is statistical inference?
  
• What is an estimator?
  
• What is internal estimate?
  
• Define type-II error.
  
• What is critical region?
  
• Define input and output devices.
  
• What is trouble shooting?

3. Write short answers to ay EIGHT questions: (2x6=16)

• What is the basic requirement for a sample?
  
• What is meant by the term `Sample Design?'
  
• Explain briefly the meaning of sampling error.
  
• Give a short account of shape of the sampling
  distribution of
  
• What do you mean by judgement sampling?
  
• Define the term `Sample Statistic'. Give an example.
  
• Distinguish between dependent and independent
  variable.
  
• What is a scatter diagram?
  
• Explain the method of least squares for fitting a
  regression line.
  
• Define the term correlation Coefficient.'
  
• Describe the properties of the correlation coefficient.
  
• If in a regression line  = a + by, x = 215. find the
  value a
  

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

• The semi -averages tor years 2003-2010 are 160 and
  120. Find trend values for the years 2003 and 2010.
  
• Define seasonal variation and cyclical fluctuation.
  
• What is meant by analysis of time series.
  
• Given Y = 1; 2, 3, 3, 6, X = 0 I, 2, 3, 4 and  = 0.6 +
  1.2 X. Show that  e12 =  2.
  
• Explain, the method of least squares in time series.
  
• Y = 7 + 0.4 X, the unit of X being one year.
  Observations are from 2002 to 2007 with origin at the
  middle of 2004 and 2005. Find the trend values up to
  year 2008.
  
• When two attributes are said to be negatively
  associated?
  
• Write down the properties of Spearman's rank             .
  correlation coefficient.
  
• Define a contingency table.

(Section —II)

5.
a) In a normal distribution, the mode and M.D. are 15
and 4 respectively.
Find
(i) P (X = 10)
(ii) P (13 < X < 16)

b)     In a normal distribution, 31% items are under 45 and
8% are over 64. Find mean and S.D.

6.
a) Take all possible samples of size three with
replacement from the population 2, 4. Show that the
population variance is thrice of the variance of sample
means.

b)     The height of 1500 students are normally distributed
with a mean 68.0 inches and S.D. of 2.5 inches If 300
random samples of size 25 are drawn from this
population, determine the expected mean and standard
deviation of the sampling distribution of means, if
sampling is done (i) with replacement (ii) without replacement          4

7.
a)  90% confidence interval for µ is constructed as (12.3,
16.7) for a normal population whose variance is 25.
Find the sample size being used irk this problem.

b)     Six college students were selected to impart special
training. They were given one month further training
and a second test of equal difficulty was held at the
end of it. The marks in two tests are given below:         4

Do the students benefit by special training? Use α = 5%

8.
a) Find out correlation coefficient from the following
data:                                                 
X:         2       4        5       6       8       11
Y:         18    15     11       8       7     ' 5

b) Given rxy — 0.8 bxy = 0.45           -                 4
What would be the value of bxy?

9.
a) Discuss the association between the parents and their.
sons with respect to their height given below.             4
Use level of significance as 0.01

b) Find the trend values by using 3-days moving average
by the following data:                    4