Statistics
Lahore Board 2015
Inter Part-II
Time: 20 Min.
Objectiv
Marks = 17
Note: Four possible answers A, B, C and D to each question are given,. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink in the answer-book. Cutting or filling two or more circles will result in zero marl in that question.

Q1

• In a normal distribution, X lies between :

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

• If Z~ N (0.1), then µ4 is equal to :

(A) 0   
(B) 1
(C) 3   
(D) ά4

• In a normal distribution, mean deviation is approximately:

(A) 2/3
(B) 2/3 α
(C) 4/5
(D) 4/5 α

• Sample is a subset of:

(A) Population
(B) Data
(C) Set
(D) Distribution

• In sampling without replacement, the number of samples is equal to:

(A) n   
(B) N
(C) Nn 
(D) [Nn]

• ΣXP(X) is equal to :

(A) n
(B) µ
(C) µẍ
(D)  N

• The estimator of µ is :

(A) ẍ
(B) X
(C) α
(D) ẍ

• Level of confidence is denoted by :

(A) α   
(B) ß
(C) 1-α
(D) 1- ß

• Which of the following is not composite hypothesis :

(A) µ≥ µo
(B) µ≤ µo
(C) µ=µo
(D) µ# µo

• In the regression y =a + bx , the y is called

(A) Independent variable       
(B) Dependent variable
(C) Fix variable          
(D) constant

• In the regression y =a + bx:

(A) Σx=Σx      
(B) Σy=Σy
(C) Σx=Σy      
(D) x = y

• The range of slope is :

(A) -1 to -1
(B) 0 to 1
(C) -α to α      
(D) 0 to α

• If   [Σd2/n(n2-1) is zero then value of rs is:

(A) 0.5
(B) -1
(C) 0   
(D) 1

• The co-efficient of association (Q) lies between :

(A) 0 & +1     
(B) -1 & +1
(C) - α to α     
(D) -1 to 0

• The graph of time series is called :

(A) Historigram          
(B) Histogram
(C) Polygon    
(D) Circle

• Movements in secular trend are :

(A) Smooth    
(B) Steady
(C) Regular    
(D) All of these

• A decimal number system has base :

(A) 10 
(B) 2
(C) 8   
(D) 16

Statistics
Lahore Board 2015
Inter Part-II
Time: 3.10 hrs
Essay Type
Marks = 83

SECTION - I

2.Write short answers to any EIGHT (8) questions:16

• Write any three properties of normal distribution.
• Define standard normal distribution.
• The mean of normal distribution is 20. What will be the value of its mode?
• In normal distribution µ = 85 , α = 4.5 , find Q3.
• In normal distribution µ = 9 , Q3 = 171 , find S.D.
• What is difference between estimator and estimate?
• Define interval estimation,
• Define type I and Type II error.
• What is test statistic?
• Differentiate simple and composite hypothesis.
• Describe the types of printer.
• Differentiate between hard and soft copy.

3.Write short answers to any EIGHT (8) questions :16

• Define the term population.
• Define the term parameter.
• What is meant by sampling?
• What is meant by sample survey?
• Define the term BIAS.
• What is meant by sampling error?
• What is meant by simple regression?
• What is meant by curve fitting?
• Define scatter diagram.
• Define the term correlation.
• Interpret the meaning when r = + 1.
• What is the limit/range of correlation coefficient (r)?

4.Write short answers to any SIX (6) questions :12

• Define positive attribute.
• Define contingency table.
• Explain coefficient of association.
• Define analysis of time series.
• Explain with examples the seasonal trend.
• Write additive model of the time series.
• Define noise.
• A straight line is fitted to a time series Y = 2 ± 1.7 X to the years (1990 - 1994) taking origin at 1990. Find trend values.
• Given Y = 13 ± 0.8 X is fitted to the years (2001 - 2005) with origin at 2003. Find estimated value for the year 2007.

SECTION-II

Note: Attempt any THREE questions.

5.(a) In a normal distribution mean is 50 and variance is 100. Find the area :4

• Below 44
• Above 37.2
• Between 29 and 53

(b) Let X~N (0,1), find : 04

• P(Z<1.5)
• P(Z>0.28) 
  
• P (0.32 <Z< 1.38)
• P (-1.2 <Z <2.1 )

6.(a) A population of four values 3, 4, 5, 6. Take all possible samples of size 3 without replacement. Make sampling distribution of mean from these samples. Compare the
mean and standard error of it with mean and standard deviation of the population.(4)

(b) Given P1 =1/3, P2=2/3, n1=2, n2=2. sampling is done with replacement. Find E (P1-P2) and S.E. (P1-P2). (4)

7.(a) Ten packets of biscuits are chosen at random and their mass measured in grams. The results are n = 10, Σx = 3978.7, Σ x2 = 1583098.3 assuming sample from normal distribution with mean mass µ, calculate. 98% confidence interval for µ.(4)

(b) If n = 50 , x = 45 where x is the number of success then test Ho: µ≤ 0.8 against  H1:π > 0.8 at 5% level of significance?  (4)

8.(a) Find regression equation of y on x to the following data : (4)

(b) Find correlation co-efficient for the following information: (4)
Σxy= 3467 x =13 y = 22
Sx = 7.73 Sy = 8.04 n = 10

9. (a) Test the association between the subject and results from the following table : (4)

(b) Calculate 7 days moving averages for the following record of attendance : (4)

SECTION -III (Practical Part)

Note: Attempt any THREE questions.

A. Draw all possible samples of two letters each without replacement from the letters of the word "PUNJAB". Find the proportion of the letter "A" in each sample. Make the sampling distribution of sample proportion and verify that µp=P  (5)

B.Find a 90% confidence interval for the mean of a normal distribution if α = 2 and a sample of size 8 gave the values 9,14,10,12, 7, 13, 11, 12.  (5)

C. The following data were obtained in a study of the relationship between the weight and chest size of infants at birth . (5)


Compute and interpret the sample correlation coefficient.

D.The students in a certain college, were divided into four groups as below: (5)


Compute the value of x2 (Chi-square) and test that there is no association between the residential status and intelligence.

E. Fit a straight line to the following data :(5)


Also estimate the value against 1992.