Inter (Part-II) Lahore Board 2014
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 normal distribution 95% of the area lies between the limits:

(A) 1.1 ±2a
(B) µ ± 1.96 a
(C) µ ± 1.6456
(D) µ t 2.58a

• In normal distribution p = 10 , a2 = 25 the mode is

(A) 5
(B) 10
(C) 25
(D) 100

• Normal distribution has parameters :

(A)    
(B)
(c)  ²
(D) , ²

• A sample is a part of the :

(A) Sampling
(B) Population
(C) Unit
(D) En-or

• A value calculated from population is called a :

(A) Statistic
(B) Parameter
(C) Mean
(D) Proportion

• The standard error increases when the sample size is :

(A) Increased
(B) Decreased
(C) Fixed
(D) Small

• If E () =  then  is:

(A) Biased
(B) unbiased
(C) Positively biased
(D) none of these

• A judge acquits an innocent person. It is an example of:

(A) Type I error
(B) Type II error
(C) Correct decision
(D) none of these

• The hypothesis which is to be tested for possible rejection is

(A) Simple
(B) Composite
(C) Null
(D) Alternative

• In the regression line of y on x :

(A)
(B)
(C)       
(D) Both B and C

• The regression line always passes through the points:

(A)  (X,Y)            
(B) ( , )
(C),Y)
(D)  ( x,  )

• If both regression coefficients are negative, then the correlation coefficient will be :

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

• If the attributes A and B are completely associated, then the coefficient of association is eaual to :

(A) I
(B) Zero
(C) -1
(D) None of these

• Both the coefficient of correlation and coefficient of association lies between :

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

• Suppose that y = 20 + 5x describes well an annual time series for 1992 - 2000. If the origin is 1996, then the trend value for 1997 is :

(A) 5
(B) 20
(C) 25
(D) 15

• Long term variations are regarded as :

(A) Secular trend
(B) Seasonal variation
(C) Cyclical variation
(D) irregular variation

• Wall clock is an example of a :

(A) Digital Computer
(B) Analog computer
(C) Disk         
(D) None of these

Inter (Part-II) Lahore Board 2014
Statistics
Part II(Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Section I

Q.2. Write short answers to any EIGHT (8) questions :.

1. Define the standard normal distribution.
2. Describe any three properties of the normal distribution.
3. Write down the points of inflection in a normal distribution.
4. In a normal distribution  = 30 and  =10. Find the mean deviation:
5. The mean of the normal distribution is 20. What will be
6. The value of its mode?
7. Define a simple hypothesis.
8. What is meant by critical region?
9. Define type I error.
10. Given  = 100 , , = 16 and  = 90, find 'z'.
11. Given s21; = 1.43 , s22 = 5.21. n1, =10 , n2 = 10, find the "SP"
12. Differentiate between hard copy and soft copy.

Q.3.Write short answers to any EIGHT (8) questions :

• What is sampling frame?
• Differentiate between parameter and statistic.
• Define existent population.
• How can you define sampling distribution?
• Define regression analysis.
• What is the main purpose (object) of sampling?
• Distinguish between regressor and regressand.
• Suppose the estimating equation  = 5 - 2x has been calculated for a set of data. Find the y-intercept and slope of this line.
• Find population mean "" and population variance "",if samples of size '2' with replacement give mean and variance of 10 and 2.5 respectively.
• Describe perfect positive correlation.
• For a given set of data the two estimated regression lines are :  =16.2 - 0.785 y and  = 20.8 - 0.219x, find product moment correlation co-efficient.
• Give two examples of correlation.

Q.4.Write short answers to any SIX (6) questions :

• Define association of attributes.
• If (A) = 20 , (B) = 10, n = 40, find (AB)
• What is time series?
• Define positive association and negative association.
• Define signal and noise.
• What are the main components of time series?
• Define the secular trend.
• What is meant by residual?
• Given (A) = 340000, (B) = 6000, (AB) = .5300 , n = 70000, whether attributes A and B are positively associated.

Section-II
Note: Attempt any THREE questions.

Question #5
(a) Assume the mean height of soldiers to be 69 inches with a variance of 9 inches. How many soldiers in a regiment of 1000 would you expect to be over six feet tall? 
(b) The heights of a large sample of men were found to be approximately normally distributed with mean 67.56 inches with standard deviation 2.57 inches. What height is exceeded by 5% of the men?     

Question #6
(a) If the size of the simple random sample from an infinite population is 36, and the standard error of mean is 2, what must be the size of the sample becomes if the standard error is to be reduced to 1.2?     
(b) Given the following information : 4.
         =36                     

Find the mean and standard error distribution of the difference (1- 2  )

Question #7
(a) Ten packets of a particular brand of biscuits are chosen at random and their mass was measured in grams such that n = 10 , x = 3978.7 , ∑x2 = 1583098.3. Calculate 98% confidence interval for population mean .      
(b) For the data given. in (a) part, test the null hypothesis Ho : = 400 grams at 2% level of significance.       

Question #8
(a) Given the following data"

Show that : (i) ∑y = ∑ (ii) ∑e, =0    for  = a + bx
(b) (i) For a given set of data, we have r = 0.48, sxy = 36, s2x = 16. Find sy,. = 11.8+2x
(ii) Given that , find correlation co-efficient.  = -5.5+0.5y

Question #9
(a) Test the independence between level of intelligence and social status at  = 0.05         

(b) The following is the data for the years 1960-73: 

Calculate 7-years moving average.

Attempt any three Parts Section-III ( Practical Part )

(A) (i) Take all possible sample of size 2 without replacement from the population 2, 6, 8, 12
(ii) Form sampling distribution of means and verify that Var ()

(B)Take all possible sample of size 2 with replacement from the finite population 2, 3, 4, 5 and show that sample mean is a unbiased estimator of the population mean.

(C) compute the co-efficient of correlation:

 (D)Find the value of Chi-square from the following data and test the hypothesis that there is no relation between the level of intelligence and the social status. Use a 0.05    

(E)       Find the tre id values by the method of least square : 5