RAWALPINDI BOARD 2016
PAPER STATISTICS
PART-II
Time: 20Min
(Objectice 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,Cor D with pen or marker in front of that question number.

•    Two attributes A and B are independent if (AB) =

(a) Independent
(b) Disassociated
(c) Positively associated
(d) Difficult to tell

• In time series, seasonal variation is in:

(a) Short term
(b) Long term
(c) Irregular term
(d) None of these

• If a straight line Y=a+ bX is fitted to the time series data then:

• In computer studies DOS stands for:

(a) Data Operating system
(b) Disk of System
(c) Data of Support 
(d) Disk Operating system

• If X—N(100,64) then standard deviation (a) is:

(a) 100
(b) 64
(c) 8
(d) 10

• If Z~N (0,1) then µ4 is equal to:

(a) Zero
(b) 3
(c) 1
(d) α4

• P(Z<O) is:

(a) 0.6 
(b) , 1
(c)   Zero  
(d)  0.5

• Probability distribution of a statistic is called:

(a) Sampling  
(b) Parameter
(c) Sampling distribution
(d) Data

• In sampling without replacement, an element can be chosen in the sample:

(a) Less than one
(b) More than once
(c) Only one 
(d) Difficult to tell

• In sampling with replacement, the number of samples will be:

(a) Nn
(b) nN
(c) N 
(d) (Nn)
                       

• The process of estimating single value of unknown parameter is called:

(a) Inteival estimation
(b) Point estimation
(c) Confidence interval
(d) Hypothesis

• If ɵ is estimator of ɵ, then ɵ) is called unbiased if:

(a) E (ɵ) > ɵ
(b) E(ɵ)< ɵ
(c) E (ɵ)# ɵ
(d) E(ɵ)=, ɵ

• If Ho is true and we reject H0 then it is:

(a) Type-II error
(b) Standard error
(c) Sampling error
(d) Type-I error

• In regression the sum of errors i.e. Σ(Y-Ý) is:

(a) Zero
(b) < 0 
(c) > 0
(d) # 0

• If Ý= bX then 'a' is:

(a) Non-negative
(b) Negative
(c) Zero      
(d) Slope

• The sample correlation co-efficient is denoted by

(a) P
(b) r
(c) b         
(d) ß

Time: 2:40 Hours
(Subjective Part)
Marks: 68
SECTION-I

2. Write short answers of any Eight Parts.16

• Write down probability density function of normal distribution.
• What is relationship between quartile deviation and standard deviation of normal distribution?
• How are standard deviation and mean deviation of normal distribution related with each other?
• What are values of ß1 & ß2 for normal data? Interpret it.
• Discuss points of inflexion of normal distribution. Are they equidistant from mean?
• What is pooled estimator of variance?
• Find pooled estimator of population proportion.
• Define interval estimation.
• Define hypothesis testing, null and alternative hypothesis.
• What is t-statistic?
• Name some hardware components of a personal computer.
• Name some software components of a personal computer.

3. Write short answers of any Eight Parts.16

• What is sampling distribution?
• Define standard error of proportions.
• Differentiate sampling with and without replacement.
• Enlisth the two advantages of sampling.
• If ά = 4 , N = 9, n = 3 find άx for sampling without replacement.
• Given N = 400, n = 100, άx =35, if sampling is done with replacement. Find S.D. of population.
• For the regression lines y =15-1.96x , x = 9 — 0.5y calculate value of by.x and bx.y .
• If rxy= 0.5, bxy=0.7 , find by.x.
• If Sxy = 20, S2x=10 , rxy = 0.6 find Sy
• Write two properties of correlation coefficient.
• What would be the value of rxy if ryx = 0.87
• If sx=10,Sy =10, rxy=0.6 find by.x

4. Write short answers of any Six Parts.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 + 0.8X is fitted to the years ( 2001 -2005) with origin at 2003. Find estimated value for the year 2007.

SECTION-11

Atempt any THREE questions Each question carries 8 marks

5.(a) The mean and standard deviation of normal distribution are 100 and 20 respectively. Find area:04

• Between 65 and 85
• Between 65 and 125

(b).Find two points having 98% of the area between them. 04

6.(a)Suppose a random sample of size "n" is taken from a population of size "N". Assume n = 1 compute αx; if sampling is done:04

• with replacement
• without replacement

(b) A small professional society has N = 4500 members. The president has mailed n= 400 questionnaires to a random sample of members asking whether they wish to affiliate with a large group. Assuming that the proportion of the entire         membership favouring consolidation is p = 0.7. Find the mean and Standard error of the sample proportion p . 04

7.(a) Give the following information n = 12, X =209, S=35 . Find 95% confidence interval- for the population mean (µ) . 04

(b) Given the following information: n = 16, X =11, S2=81. Test the hypothesis that mean of the population is more than 10. 4

8.(a) From the following results show that 'r' is the geometric mean of two regression coefficients:04
                Σ(x-x) = 80 , (y-Ý)2=170 , Σ (x-x)(y-y) = 100

(b) The correlation coefficient for sample of 20 observation is 0.6, if x=12, y=20, sx=2. Estimate the line of regression of y on x.04

9.(a) Using a 5% level of significance, test whether there is any connection between the beaches and sex?04

(b) Fit a straight line y =a+bx and find y when x=70: 04        

SECTION-III (Partical Part)

Note:Attempt any three questions.10

• A random variable x has the following probability distribution:         

(a) Find mean, variance and standard deviation of population.

(b) If a sample of size 16 is drawn with replacement from this population then find mean and standard error of sampling distribution of x .

• Assume the experimenter has no preconceived notions about which formula might be better:

Test at 5% level of significance that mean of pop-1 equal to the mean of pop-II

• Fit a least square line to the following data taking x as dependent a   variable:       

• Find value of chi-square x to test the irradiation between attributes:

• Calculate 7-day moving averages for the following record of attendances: