RAWALPINDI BOARD 2014
PAPER STATISTICS PART-I
(Objective Part)
Time: 20 Minutes       Marks: 17

Note: You have four choice 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.

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

(a)  
(b)
(c)
(d)

• (ii)If (AB) < then the two attributes are:

(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 Ŷ=a+bx is fitted to the time series data then:

(a) ∑Y < ∑Ŷ 
(b) ∑Y = ∑Ŷ 
(c) ∑Y ≠ ∑Ŷ
(d) ∑Y > ∑Ŷ

• 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 (σ) 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) σ⁴

• P(Z<0) 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) n^N
  (c) N   
  (d) (N_n)

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

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

• lf Ô is estimator of O , then Ô is called unbiased if:

(a) E(Ô)>O
(b) E(Ô)<O
(c) E(Ô)≠O
(d) E(Ô)>O

• If H_o, is true and we reject H_o 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. ∑(Y-Ŷ) is:

(a) Zero         
(b) < 0
(c) > 0
(d) ≠ 0

• If Ŷ= bX then 'a' is:

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

• The sample correlation co-efficient is denoted by:

(a) ρ
(b) r    
(c) b   
(d) β

Inter (Part-I) Rawalpindi Board 2014
Statistics
Part I s(Subjective)
Time Allowed: 3.10 Hours 
Max. Marks: 83

SECTION-I

2. Attempt any EIGHT short questions.

• 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 β₁& β₂ 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 come software components of a personal computer.

3. Attempt any EIGHT short questions.

• What is sampling distribution?
• Define standard error of proportions.
• Differentiate sampling with and without replacement.
• Enlish the two advantages of sampling.
• If σ=4 , N=9 , n=3 find σ₈ for sampling without replacement.
• Given N=400 , n=100 , σ_x=35 , if sampling is done with replacement. Find S.D. of population.
• For the regression lines ŷ=15=1.96x , x=9-0.5y calculate value of b_y,x and b_x,y.
• If r_xy = 0.5 , b_xy = 0.7 , find b_y,x.
• If S_xy = 20 , S_2x = 10 , rxy = 0.6 find Sy
• Write two properties of correlation coefficient.
• Whai would be the value of r„ if r..„ =0.87
• If 5, = KS, = 10, r, =0.6 find b,„,,

4. Attempt any SIX short questions.

• Define positiee 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-II

Attempt any THREE questions.. (8 X 3 = 24)

Question #5 
(a) The mean and standard deviation of normal distribution are 100 and 20 respectively. Find area:
(i) Between 65 and 85
(ii) Between 65 and 125     
b) Find two points having 98% of the area between them.

Question #6 
(a) suppose a random sample of size "n" is taken from a population of size "N". Assume  compute 2, if sampling is done:
(i) with replacement          
(ii)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 .

Question #7 
a) Give thc following information n = 12,  209, =35. Find
95% confidence interval for the population mean (μ).
b) Given the following information: n = 16, g ==11,²=81 Test the hypothesis that mean of the population is more than 10.

Question #8
a) From the following results show that 'r" is the geometric mean of two regression coefficients:

b) The correlation coefficient for a sample of 20 observation is 0.6, if =12,=20,sz = 2, Estimate the line of regression of  on .

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

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

SECTION –III:

Attempt any THREE Parts.

 (i) A random variable x has the following probability distribution:

 (i)       Find mean, variance and standard deviation of population.
(ii)       If a sample of size 16 is drawn with replacement from this population then find mean and standard error of sampling distribution of .
(ii) Assume the experimenter has no preconceived notions about which formula might be better:

Test at 5% level o significance t at mean of pop- qal to the mean of pop-II
(iii) Fit a least square line to the following data taking x as dependent variable:

(iv)Find value of chi-square x to test the irradiation between attributes:

(v) Calculate 7-days moving averages for the following record of attendances: