Inter (Part-II) Faisalabad Board 2016
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.

• Mean of standard normal variable is:

(a) µ   
(b) 1   
(c) 0    
(d) 2

• Shape of normal distribution is:

(a) Positively skewed
(b) Negatively skewed
(c) Symmetric
(d) Flat

• Maximum ordinate of normal distribution is:

(a)           
(b) 
(c)
(d)

• Total number of samples with replacement are:

(a) Nn
(b)
(c) N   
(d) n

• Total number of samples without replacement are:

(a) Nn
(b)
(c) N   
(d) n

• For sampling distribution of sample variance, S2=. with replacement is:

• An estimator, , is said to be unbiased estimator o parameter 0 if:

(a) E()> θ    
(b) E()< θ
(c) E () θ   
(d) E()= θ

• Which option contains two statistics?

(a) π=
(b) µ and S2
(c) , S2
(d)

• Which is a simple hypothesis?

(a) Ho :µ > 50 
(b) Ho: µ> 50
(c) Ho :µ< 50  
(d) Ho: µ = 50

• Strength of relationship between two variables is focus of:

(a) Regression
(b) Correlation
(c) Association of attributes
(d) Business cycle

• Regression coefficient is independent of:

(a) Origin       
(b) Scale
(c) Both origin and scale        
(d) Neither origin nor scale

• Coefficient of correlation was invented by:

(a) Pearson
(b) Spearman
(c) Fisher        
(d) Gauss

• A characteristic that varies only in quality is called:

(a) Correlation
(b) Regression
(c) Attribute   
(d) Continuous

• Coefficient of contingency can take values:

(a) -1<C< +1  
(b) 0<C <11
(c) 0 < C <1    
(d) 0 <C < q = min (r ,c)

• Method of least squares can be applied to:

(a) Straight line only  
(b) Parabola only
(c) Both staright line & parabola
(d) None of these

• Method of moving average eliminates:

(a) Cyclical fluctuations only
(b) Seasonal fluctuations only
(c) Both cyclical and seasonal fluctuations
(d) None of these

• Speed of a computer is measured by:

(a) Gigabytes 
(b) Megabytes
(c) Kilograms 
(d) Gigahertz

Inter (Part-II) Faisalabad Board 2016
Statistics
Part II (Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Section I

2. Write short answers of any Eight Parts.                                                 16

• What is standard normal variable?
• A normal distribution has µ = 80, σ =36, find its mode and mean deviation.
• What is normal frequency distribution?
• Write any two properties of normal distribution.
• In normal distribution q1 = 65,q3 = 75, find its mean.
• Give the formula of biased and unbiased variance.
• Differentiate between estimator and estimate.
• Define one tailed and two taild test.
• Given µ = 5,n = 9, = 2,t = -2 , find s.
• What is meant by degree of freedom?
• What is computer?     
• What is compiler?

3. Write short answers of any Eight Parts.                                                 16

• Differentiate between parameter and statistic.
• Find µ and σ2 if sample size of 2 W.R. give mean and variance of  is 10 and 2.5 respectively.
• Define sampling frame and sampling design.
• What do you understand by simple random sampling?
• Given N = 310, n = 100, = 35 and sampling is done without replacement then find  .
• Differentiate between sampling error and non-sampling error.
• What do you understand by zero correlation.
• If bxy = -0.27 and by.x = -0.38 find rxy.
• Differentiate between positive and negative correlation.
• If rxy = -0.89 and ry.x = and ru.v where u = x - 8 and v = y + 7 .
• Write down two properties of regression coefficient.
• Define simple regression with examples.

4. Write short answers of any Six Parts.                                                                 12

• Define contingency table.
• Given (A) = 200, (B) = 800, N = 1000, find (AB) assuming A and B are independent.
• Explain the term negatively associated.
• Define the secular trend.       
• Explain signal and noise.
• What are irregular movements?
• Define the term time series.
• What is histogram?
• Explain method of moving average.

SECTION-II: Attempt any THREE functions. Each questions carries 8 Marks.

Question #5
(a) X is a normal variate with mean 1 and standard deviation 3, find the probability that 3.43 5 X 5 6.19.
(b) If X is N (24, 16), then find (i) P33 (ii) D9

Question #6
(a) Given n1 = 4,n2 = 4,σ1 = 4,N1 = 25, N2 = 25, var( 1 –  2)=10. Find σ2 when sampling is done without replacement.
(b)  If the size of the simple random sample from an infinite population is 25 and the standard error of the mean is 4. What must be the sample size if the standard error is reduced to 2? 

Question #7
(a) A random sample size n = 12 has been selected from a normal population with       unknown mean. The sample value wer 90, 45, 46, 49, 50, 55, 60, 65, 69, 70, 72 and 73. Find 90% confidence interval for population mean.
(b) In a test given to two groups of students the marks obtained were as:

Calculate the value 'of 't' and examine the significance
difference between two mean use σ = 0.05 .
8. (a) The following statistics have been computed  =14, = 22,
Sx = 6,Sy =7,r = 0.72 . Find the two regression equations.
(b) Find the coefficient of correlation for the data given:
9. (a) Discuss the association between taking tea and class status α =5%.

(b) Smooth the given data 4-years moving average:

                                                SECTION-III (Practical Part)
                                    Note: Attempt any THREE questions.
(A) A population consists of values 4, 6, 8, 10, 12. Make all possible samples of size 2 with replacement. Find mean and variance of all samples.
(B) Given two random samples from two independent normal papulations with:

Find a 99% confidence interval for (µ1-µ2). Assume that population variances are equal.
(C) Fit a regression equation taking y as dependent variable of the following data:

(D) Five sacks of coal A, B, C, D and E have different weights with A being heavier than B, B being heavier than C and so on. A weight lifter ranks the sacks in order A, D, B, E, C. Calculate rank correlation.
(E) Calculate 7-days moving averages for the following data: