2013  Statistics(Objective)
Time Allowed: 20 minutes
Paper II
Maximum 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. Attempt as many questions as given in objective type question paper and leave others blank. Use of ink remover or white correcting fluid is not allowed.

Question#1

• Fourth mean moment of Normal dist is ϭ= 4
  
  (A) ϭ²
  (B) ϭ⁴
  (C) 3µ²2
  (D) µ²2
  
  
• S.N.D has mean and variance
  
  (A) 0 ard 1
  (B) 0 and 2
  (C) 1 and 2
  (D) 1 and 0
  
  
• Proportion of cases lying between µ ± ϭ is
  
  (A) 68.26%
  (B) 95.44%
  (C) 99.73%
  (D) 100%
  
  
• Statistic is associated with
  
  (A) Population
  (B) Sample
  (C) Both a and b
  (D) None of these
  
  
• Probability dist. of sample statistic is
  
  (A) Standard error
  (B) Sampling error
  (C) Sampling dist
  (D) None of these
  
  
• Probability sampling is also called
  
  (A) Random sampling
  (B) Non-random sampling
  (C) Sampling dist
  (D) Quota sampling
  
  
• 95% C.I for π is
  
  (A)  
  (B)
  (C)
  (D)
  
  
• Rejecting of true null hypothesis is called
  
  (A) Type I error
  (B) Type II Error
  (C) Standard Error
  (D) Zero
  
  
• When population S.D is known, then test statistic is
  
  (A) Z-test
  (B) t-test
  (C) x2-test
  (D) F-test
  
  
• Regression line passes through their
  
  (A) Variances
  (B) S-Ds
  (C) Means
  (D) None of these
  
  
• A variable provides the basis for estimation is called
  
  (A) Dependent variable
  (B) Independent variable
  (C) Discrete variable
  (D) Continuous variable
  
  
• Correlation coeff is ----------------- of two regression coefficients.
  
  (A) A.M
  (B) H.M.
  (C) G.M
  (D) Median
  
  
• If (AB)<  , A and B are called
  
  (A) Independent
  (B) Positively associated
  (C) Negatively associated
  (D) None of these
  
  
• The degree of freedom in 2 x 2 contingency table is
  
  (A) 2
  (B) 4
  (C) 1
  (D) Zero
  
  
• Increase in sale before Eid is an example of
  
  (A) Secular trend
  (B) Seasonal variation
  (C) Cyclical variation
  (D) Irregular variation
  
  If y = 10+2x with origin 1982. The Equation of straight line with 1980 Is
  
  (A) y=10 + 4x
  (B) y= 14 + 2x
  (C) y = 6 + 2x
  (D) y = 6 - 2x
  
  
• Brain of the computer system is called
  
  (A) CPU
  (B) Main memory
  (C) Hard disk
  (D) Monitor
  
  Statistics
  (Subjective)
  Time Allowed: 2.40 hours
  Paper (II)
  Maximum Marks: 68

SECTION: 1

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

• Define the Normal distribution.
• Give four properties of Normal  distribution.
• For a Normal distribution with µ=0 and ϭ2=1 for what are apper and lower quartiles? (iv) Write down the importance of Normal distribution.
• What is tit shape of Normal Curve, made its graph
• What is unbiasedness?
• Define confidence Interval.
• What is one-tailed test and two-tailed test?
• Define significance Level.
• What is Acceptance region?
• Differentiate between Hardware and software in the computer
  
• What is mini computer?

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

• Define random sampling
  
• Distinguish between parameter and statistic.
  
• Define standard error.
  
• Define Non Probbability sampling
  
• Explain sampling error.
  
• Describe any two advantages of sampling.
  
• How many variables are involved in simple regression?
  
• Write two properties of regression coefficient.
  
• If y =110 + 1.78 x then find y given x = 90 and 100
  
• Define correlation.
  
• write any two properties of (r)
  
• Let Σ(x –x)²=14 Σ(x-x)(y-y=8 Σ(y-y)²=10 find value of r.

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

• Sketch 3 x 3 contingency table using two attributes A and B.
  
• If (A) = 20 , (B)= 10 , (AB) -5 and N = 40. Find (Aß), (άß) and (άß)
  
• Name the components of time series
  
• Describe method of least-Square.
  
• Narne four phases of a business cycle.
  
• Define time series with two examples.
  
• If least-square lines one y on x and the other x on y are: y = x - 10 and x = 10- y, find x and y.
  
• A trend line (y=100-10x is fitted to time series 2007 to 2011 (both inclusive with origin at 2009. Find the tend values for the year 2007 to 2012.
  
• What is noise with reference to time series

SECTION II

Note: Attempt any three questions, Each question carries equal marks.  (8x3=24)
Question#5
(a) Give a normal distribution with µ=40) and ϭ=6 Find
(i) The area below 32
(ii) The arts above 27
(b) In a normal distribution the mean and standard deviation are 0 and 1, respectively.
Write down its equation and find the value of maximum ordinate correct to four
decimal places

Question#6
(a) A population consists of 2,2,4,6,8. Compute mean and standard error of samp1ing distribution of means if n=2 and sampling is done 'without replacement
(b) Given N₁=3, n₁=2, P₁=1/2   ;     N₂=3, n₂=2, P₂= 1/3
Find the mean and standard error of the sampling distribution of P1-P2 if sampling is done:
(i) With replacement
(ii) Without replacement

Question#7
(a) Two random and in dependent samples of size n1 = 11 and n2=14 from two normal
x₁=75, Σ(x-x)²=372
y=60, Σ(y-y)²=365
populations give the following results
Find 99% confidence interval for (µ1-µ2), Assume that two population variances are equal.
(b) Ten students spend the following time in hours of their studies during a week 35,40,17,23,50,45,30,20,18 and 22. Test the hypothesis µ ≤ 20 at ά =0.05.

Question#8
(a) Show that the sum of errors and sum of' squares of errors are zero by fitting y=a+bx

(b) Given n = 100, Σx=5000, Σy=6000, Σxy=300300, Σx²=250400, Σy²=360900 Calculate S_x,S_y and r.

Question#9
(a) Test whether there is any association or not at 5% level from the data of education and gender:

(b) Fit linear trend from the given information for the years 1990 to 1996.
Σx=0, Σx²=28, Σy=2450, Σ xy=660