Gujrawala Board 2016
Statistics
Inter (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.

• If ∑(x-)(y-) is zero then the regression coefficient y on x will be:

(A) More than zero
(B) Less than zero
(C) Exactly zero
(D) None of these

• If H₁ is given by b > b_o we will use test:

(A) Two tail.
(B) One tail
(C) Three tail
(D) None of these

• The term samie space is used for:

(A) All possible outcomes
(B) Sample
(C) Sample design
(D) Sampling

• For a least square linear trend y =-7 a ± ox :

(A) ∑=∑ y          
(B) ∑e=0
(C) ∑y- =()         
(D) all of these

• In a normal distribution, all odd ordered moments about mean are equal to:

(A) One
(B) Zero
(C) Additive
(D) None of these

• 1624 MB equal to:

(A) 01 RB
(B) 01iB
(C) 01 TB
(D) 01 Byte

• Fire in a factory is an example of:

(A) Secular trend
(B) Irregular trend
(C) Cyclical variation
(D) Seasonal variation

• The number of cells in 4x3 contengency table are:

(A) 6
(B) 8
(C) 12
(D) 1

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

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

• In a normal distribution p.=10 and 62 = 25 , then mode is:

(A) 5
(B) 10
(C) 25 
(D) 100

• In a normal distribution N (µ, σ²),µ₄ is equal to:

(A) σ⁴ 
(B) 3 σ⁴
(C) σ ⁴
(D) σ² /2

• The probe distribution of statistic is called:

(A) Sampling
(B) Parameter
(C) Data
(D) Sampling distribution

• The point of estimator µ is:

(A)
(B)
(C)
(D) None of these

• If σ²=5, n=2 and sampling with replacement then σ

 (A) 2
(B) 2.5
(C) 3
(D) 5

• Two attributes A and B are independent if:

(A) (AB) = (A)(B)/n
(B) (AB)>(A)(B)/n
(C) (AB) < (A)(B)/n
(D) (AB) (A)(B)/n

• If r_xy =0.8, then r_yx :

(A) 0.4
(B) 0.8
(C) 0.64
(D) 0.10

• If H_o is false and we reject Ho, it is called:

(A) Type I error
(B) Type II error
(C) No error
(D) Both type I and type II error

Gujrawala Board 2016
Statistics
Inter (Part-II)
(Subjective)
Time Allowed: 2.10 Hours 
Max. Marks: 83
SECTION - I

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

2. Write short answers to any EIGHT questions: (2x8=16)

• Define the normal probability density function.
• Define the points of infletion in a normal distribution.
• A normal distribution has the mean µ= 85 and G = 4, find the values of Q₁ and Q₃ .
• In normal distribution find M.D and S.D if mean 50 and S.D is 10.
• If second moment about mean is 4. Find µ₃ and µ₄ of normal distribution.
• Explain the terms estimate and estimator.
• Define a point estimate.
• Describe the interval estimate.
• Describe the hypothesis.
• Define the acceptance region.
• What are the output devices in computer?
• Describe RAM.

3. Write short answers to any EIGHT questions: 2x8=16

• What do you know about population?
• Define the term parameter.
• Explain a sampling distribution.
• Give two advantages of sampling.
• What is a sample design?
• Define random sampling.
• Define slope of regression line.
• What is the value of sum of residuals/errors, in case of straight line?
• What is meant by scalier diagram?
• Interpret the meaning of r = + 1.
• Write symmetric property of correlation co-efficient.
• Find correlation co-efficient from the following equations:
   = 3-0.38X,  =1.5 - 0.27y

4. Write short answers to any SIX questions: 2x6=12

• Explain positive and negative class.
• Define class frequency.
• Differentiate between association and correlation.
• Define time series.
• Differentiate between signal and noise.
• Define irregular variation.
• Write down various methods of measuring secular trend in time series.
• Define moving averages.
• Given  =128 +4x and X =-13, -2 ,-1, 0, 1, 2. 3. Find ∑=?

SECTION - II

Question #5
(a) If xN(50,σ²⁾ value of the standard deviation, G. (4)
(b) if x a N(24, 16) and P(x<60.6)=0.983, find the value of the standard deviation, σ. (4)

Question #6
(a) If the size of the simple random sample from an infinite population is 55, the variance of the sample mean is 27. What must be the standard error of sample mean if n=165. (4)
(b) A population has the values as 2, 3, 5. Take all possible samples of size 2 with replacement and verify that: (4)

Question #7
(a) A random sample of 500 workers of the labour force in a certain region showed that 40 were unemployed. Construct the 95% confidence interval for the unemployed people in the region. (4)
(b) The lives in hours of 6 bulbs were found to be 1260, 1075, 1150, 1050, 1240, 1300. Test the hypothesis that the mean life in the population of bulbs is 1200 hours. Use α= 0.05. (4)

Question #8
(a) Find the regression line of Y on X r from the following data: (4)
∑x = 17.6, ∑Y = 32.8, ∑XY = 94.7.
∑X ² =49.64, ∑Y ² = 182, n=8 w
(b) Show that
R_xy =ruv

Question #9
(a) Find. co-efficient of association from the following data: (4)

(b) Calculate trend values by semi average method: (4)

SECTION-III Practical

Question #10
(a) Taking all possible samples of size 2 with replacement from the population 1,3,5,7. Show that (5)

(b) Compute 95% confidence interval of population mean from the information that sample mean = 50, n = 400 and population variance = 100. (5)
(c) Compute the co-efficient of correlation: (5)

(d) Out of 900 persons 300 were literate and 400 travelled beyond their district. 205 of literate also travelled. Is there any association between travelling and literacy? (5)
(e) Compute 3-years moving averages from the data given below: 5