Inter (Part-II) Faisalabad Board 2015
Statistics
Part II (Objective Type)
Time Allowed: 20 Minutes 
Max. Marks: 17

Note: You have four choices 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.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• In normal distribution the value of β₁ and β₂ are :

(A) 0 and 3
(B) 3 and 0
(C) 0 and 1
(D) 1 and 3

• In normal distribution 95 % of the area lies between the limits:

(A) μ±2?
(B) μ±1.96?
(C) μ±1.645?
(D) μ±2.58?

• In normal distribution 95% of the area lies between the limits:

(A) μ±0.7979?
(B) μ±0.6745?
(C) 0.5?
(D) 0.75?

• A value calculated from population is called:

(A) Statistic
(B) Mean
(C) Parameter
(D) Proportion

• When sampling without replacement then μ_g2-g1 is equal to:

(A) μ_{1 -} μ₂
(B) μ_{2 -} μ₁
(C) μ_{2 +} μ₁
(D) μ_{1 +} μ₂

• In sampling without replacement the relation hold is:

(A) n<N
(B) n<N
(C) n>N
(D) n> N

• A specific value calculated from sample is called:

(A) Estimator
(B) Estimate
(C) Estimation
(D) Bias

• How many types of estimation are:

(A) One
(B) Three
(C) Two
(D) None

• Accepting H₀ when H₁ is true is a:

(A) Type I error
(B) Type II error
(C) Correct decision
(D) None of these

• In case of correlation both variable x and y are used to be:

(A) Fixed
(B) Unknown
(C) Known
(D) Random

• If both regression coefficients are negative then the correlation coefficients will be:

(A) Negative
(B) Positive
(C) Zero
(D) 1

• The graph showing the paired points of (x,y) is called:

(A) Histogram
(B) Historigram
(C) Scattered diagram
(D) None

• The total area under the curve of a chi-square distribution is:

(A) One
(B) -α to 0
(C) 0 to α
(D) – α to +α

• The value of chi-square may be:

(A) Zero
(B) Positive
(C) Negative
(D) A & B but not C

• The difference between the actual and trend value is called:

(A) Slope
(B) Residual
(C) Intercept
(D) Sum of residual

• Methods of secular trend are:

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

• Which one is not an output device?

(A) Monitor
(B) Scanner
(C) Printer
(D) Modem

Inter (Part-I) Faisalabad Board 2015
Physics
Part I (Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83 

Note: Section I is compulsory. Attempt any three (3) questions from Section II and any three (3) parts from Section-III

SECTION - I

2. Write short answers of any Eight Parts. 16

• Write any four properties of normal distribution.
• Write the p.d.f.,of normal probability distribution.
• What is the relationship between binomial distribution and normal distribution?
• Find (a) P(μ- ?<X< μ+ ? ) (b) P(μ- 2?<X< μ+ 2?)
• In a normal distribution μ₄ = 243, find μ₂ and μ_3.
• Explain the term unbiasedness.
• Define interval estimation.
• Describe critical region.
• Elaborate the term type-I error.
• Given s₁² = 1.43, s₂² = 5.21, n₁=10,find s_p
• Define the central processing unit..
• What is meant by byte?

3. Write short answers of any Eight Parts. 16

• What is sampling distribution?
• Define standard erroe of proportions.
• Differentiate sampling with and without replacement.
• Enlist the two advantages of sampling.
• If ? =4 , N= 9,n=3 find ? _g for sampling without replacement.
• Given N=400,n=100, ? _g =35,if sampling is done with replacement.Find S.D of population.
• For the regression lines yˆ=15- 1.96x , xˆ=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 , s²_x=10,r_xy=0.6 find s_y.
• Write two properties of correlation coefficient.
• What would be the value of r_xy ifr_yx =0.87
• If S_x= 10,s_y = 10, r_xy=0.6 find b_y.x.

4. Write short answers of any Six Parts. 12

• Define the term attribute.
• Define the term contingency table.
• Define the term rank correlation.
• Define the term time series.
• Define the term historigram.
• What is meant by term signal?
• Name the four components of time series.
• Define the term secular trend.
• What is meant by the term seasonal variations?

SECTION-II: Attempt any THREE questions. Each questions carries 8 marks.

Question #5
(a) In a normal distribution MD=3.9895 then find four moment about mean and quartilr deviation. 04
(b) If X~N (50,10)then find (i)P(x<40) (ii) P(x>70) 04

Question #6
(a) A population consists of valued 20, 24, 28, 32, 36.By tally all possible samples of size 2 without replacement show μ_g= μ , ?²_g = ?²/n,N-n/N-1 04
(b) By taking all possible samples of size 2 without replacement of the population 1, 2, 3, 4.Find the mean of the sample distribution of variances. 04

Question #7
(a) A random sample of 400 adults and 600 teenagers,watched a certain television programme.300 adults and teenagers linked it. Construct 99% C.I. for different proportions of all adults and all teenages who watched programme. 04
(b) Given two samples of size n₁=11,n₃=14, x¯₁=75,x¯₂=∑(x1- x¯₁)2 =3721, ∑( x¯₂- x¯₂)2=365.17.Test hypothesis μ₁₌ μ₂ at α=0.01.

Question #8
(a) Estimate the regression line of y=a+bx for the following data

(b) For a sample of 20 pairs of values we have n=∑ xi=983, ∑ xi²=61339, ∑ yi²=983, ∑ xiyi= .Find the correlation coefficient for the data.

Question #9
(a) Find Spearman’s rank correlation coefficient for the following data:

(b) Find 3-year moving average to the following data:

SECTION-III (Practical Part)

Note: Attempt any THREE questions.

Question #10
(i) A random variable x has the following probability distribution:

• Find mean, variance and standard deviation of population.
• If a sample of size 16 is drawn with replacement from this population then find mean and standard error of sampling distribution of x¯.

(ii) Assume the experimenter has no preconceived notions about which formula might be better:

Test at 5% level of significance that mean of pop-I equal 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-day moving averages for the following record of attendances: