Sargodha Board 2012
Statistics
(Objective) Paper
Time Allowed. - 20 minutes
Maximum Marks:-17
Note: You have foot choices for tacit objective type question as 11, C and D. The choice which you Sink is correct; 50 lot cycle in front of that question number. Attempt as many question as given in Objective type question paper and leave others blank. Write the letter A, 3, C or I) in the column (*rite correct option) against each question. If there is a contradiction in the bubble and hand written answer, bubble option will be considered correct

• In normal distribution σ= 4 .What would be value of 4th moment about mean?

(A) 225
(B) 256
(C) 500
(D) 764

• The value of β₂ in a normal distribution is

(A) ZERO
(B) 1
(C) 2
(D) 3

• The range of normal distribution is

(A) 0 to∞
(B) a to b 
(C) -∞ to 0
(D) -∞ to + ∞

• In slagging without replacement, the samples are selected as

(A) (N-n)
(B) Nⁿ
(C) None
(D) (N_n)

•  If X=10 and µ = 12 then sampling error is

(A) 10
(B) 22
(C) 12
(D) 2

• A survey conducted by a sampling design u oiled

(A) Population survey
(B) Biased survey
(C) None
(D) Sample survey

• The kind’s estimation are

(A) 5
(B) 4
(C) 3
(D) 2

• The end of confidence interval are called

(A) Population survey
(B) Biased survey
(C) Sigma limits
(D) Confidence limits

• What would be die decision if we reject H_o when it is true?

(A) Type 2^nd error
(B) No error
(C) None
(D) Type I- error 

• What would be the value of r_xy if r_yx = 0.87

(A) 1.87
(B) 0.64
(C) 0.13
(D) 0.87

•  IF 6 ^d2 = n (n²-1) then the spearman’s rank correlation coefficient is equal so

  (A) ZERO
  (B) -1
  (C) None
  (D) 1

• What would he the value of “r” if b_yx, = 0.76 and b_xy =- 0.82

(A) -0.794
(B) -0.82
(C) Both 
(D) -0.78

• The total is ink: the curve or a xi distribution is6
  

(A)  - ∞ to 0
(B) a to b
(C) -∞ to +∞
(D) 0 to ∞

• The shape of x² distribution depends on

(A) Parameter
(B) O
(C) None
Degree of freedom

• An era of prosperity is an example of

(A) Swam vend
(B) Seasonal trend
(C) Regular trend
(D) Cyclical variation

• The manila of normal equation in case of second degree parabola are

(A) One
(B) Two
(C) Four
(D) Three 

• The bale of octal system is

(A) 10
(B) 2
(C) 16
(D) 8

Statistics
Time Allowed: 2.40 hours
Maximum Marks: 68

(Subjective)

• Write down the equation of normal curve with mean = 0 and 8 =1 .
• In a normal distribution p=163andQ, =171, find the value of Q.
• What are the values of μ, andμ₄, for a normal distribution?
• Find maximum ordinate of normal distribution when μ=10 and8 =5.
• The second moment about mean of a normal distribution is 25. Find μ₄
• What is estimation?
• What is confidence coefficient?
• What is confidence internal for μ when 8 is known and n is less than 30 and α=0.05.
• Define composite hypothesis.
• What is type-I error?
• Define high level language.
• Differentiate between analog computer and digital computer.

3.Write short answer of any eight parts. 8x2=16

• Differentiate between sample and population.
• Define random sampling.
• What do you mean by simple random sampling.
• Define sampling distribution.
• Explain the sampling frame.
• If σ²₃ =120 Find n
• Write the properties of regression line
• If Y = 3x + 10 Find slope and Y - Intercept.
• Define regression analysis.
• If byx =0.6 and y= 0.5 Find bxy
• Write down the two properties of correlation coefficient.
• If Y = 3x 10 and X = 20+ 0.1y Find . r.

4. Write short answer of any six parts. 6x2=12

• What are the different componant of time series?
• Write a short note on the secular trend. 
• What are the main phases in case of Cyclical Variations?
• Explain the method of Least-Squares.
• Lct =0, =26.1, =30.9, and = 340. Find the, value of b.
• Write down the layout of 3 -- years moving averages in case of the method of moving averages.
• Explain the coefficient of contingency.
• Write down the theoretical formula for two attributes C and D being independent. 
• Given (AB) = 150, (αB) =106, (αβ)=272,(αβ)=1132, and n =1660, Find the value of coefficient of association.

SECTION----II

Note: Attempt any three questions. Each question carries equal marks. (8 x 3 = 24)

Question#5
(a) 'X' is a normal variate with mean 30 and standard deviation 5. Find the probability that

• (26 ≤ x ≤ 40
• lx-30|< 5 5

(b) The continuous random variable X is normally distributed with mean 14 and standard deviation & . Given that P(x < 53) = 0.04 and P(x < 65) = 0.97 Find the inter quartile range. 3

Question#6
(a) The r.v.x has the following probability distribution.

X f(x)
4 0.2
5 0.4
6 0.3
7 0.1
Find the μ_x and S.E (x?) for a random sample of 36. 4

(b) A population consists of "A,E,I,O,U" Draw all possible samples of size 3 letters from this population. Find proportion of the word " 0 " in the sample. Find frequency distribution of the sample proportion. Verify that S.E=, Where P = Population proportion. 4

Question#7
(a) An electric company claimed that atleast 90 % of the parts which is supplied conformed to specifications. A sample of 500 parts was tested and 60 did not meet specifications. Can we accept company's claim at 5 % level of significance?

(b) A random sample of size n = 225, selected without replacement from a population of size N = 1500 with σ = 20,the sample mean is found to be x=100. Construct 90 % and 95 % confidence intervals for true mean of population.

Question#8
(a) The following data represent weekly sales levels of retail outlets for the 1 week period before and after a special promotional campaign. Retail outlet: 1 2 3 4 5 6 7

Sale before campaign: 18 16 21 19 12 23 26
Sale after campaign: 21 17 22 18 16 28 26
Compute the spearman's rank correlation co-efficient for this data set.

(b) If the straight line fitted to the data for the years 1987 to 1993 (both inclusive) with origin at 1990 and unit of measurement 'for x is one year is Y=600 + 75x.Find the trend values corresponding to the years 1987 to 1993. What would be the equation of the straight line by shifting the origin to the year 1987.

Question#9
(a)The following data is collected to view, is there any association between sex and colour choice.

Test whether, there is any association between sex and colour choice at α =0.05.

(b) Compute 3 - year - moving average trend from the following time series: