Statistics
Paper II
(Objective Type)
Inter –A – 2016
Time Allowed: 20 Minutes
Inter (part-II)
Maximum Marks: 17
Session (2012-14),(2013-15),(2014-16)
Note: Four possible choices A,B,C,D to each question are given , Which choice is correct, fill    that circle in front of that question Number line marker or pen to fill the circles. Cutting or filling two or more circle will result in zero marks in that question.

Q.1

• In a Normal Distribution the value of β1 and β2 are:

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

• In a normal Distribution if Mode = 50, then the value of Median is:

(A) 40
(B) 50
(C) 30
(D) 60

• Normal Distribution is:

(A) Uni Modal
(B) Tri- Modal
(C) Bi- Modal
(D) Multi- Modal

• If ∑x = 18 , N = 3 then µ is:

(A)  9
(B) 6
(C) 3
(D) 10

• A complete list of element in a population is called:

(A) Population
(B) Sample Design
(C) Sampling Unit
(D) Sampling Frame

• If  = 12 and µ = 10, then sampling Error is equal to:

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

• Confidence coefficient is denoted by:

(A) α
(B) B
(C) 1- α
(D) 1-β

• Power of test is denoted by:

(A) α
(B) β
(C) 1- α
(D) 1-β

• A hypothesis which is completely specific the population parameters:

(A) Null
(B) Simple
(C) Alternative
(D) Composite

• When value of bxy is negative, then byx is:

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

• The value of “r” is zero if:

(A) Var (x) =0
(B) Covariance (x, y) =0
(C) Var (y) =0
(D) None of these

• Correlation coefficient is independent of:

(A) Origin
(B) Scale
(C) Both A and B
(D) None of these

• For two independent attributes Q = :

(A) +1
(B) 1
(C) Zero
(D) -1 to +1

• For 3 x 4 contingency table the degree of freedom will be:

(A) 6
(B) 12
(C) 4
(D) 3

• A fire in a factory delaying production is a:

(A) Seasonal variation
(B) Long Term variation
(C) Random variation
(D) Cyclical variation

• The sum of square of residual is denoted by:

(A) ∑e
(B) ∑e²
(C) ∑e³
(D) None of these

• Drag and drop is a term associated with:

(A) Mouse
(B) Key Board
(C) Printer
(D) Scanner

Statistics (Subjective)
Inter - A – 2016
Inter (Part - II)         
Time = 3:10 Hours
Total Marks: 83
Session (2012 - 14) (2013 - 15) (2014 - 16)
It is compulsory to attempt (8-8)parts each from Q.No.2 and 3 while attempt any 6 parts from Q.No.4 and attempt any (03) questions from part- II while from section -III (practical part) (03)parts should be attempted Write same question No. and its part No as given in the question paper.22x2=44
(Section - I) 

Q.2

• The mean deviation of a normal Distribution is 16 find the approximate value of variance.
• Write down any two properties of normal Distribution.
• What is standard normal variety?
• Define the point of inflation
• Define type 1 error with example
• What is unbiased Estimator?
• Differentiate between Simple Hypothesis and composite Hypothesis.
• Write the lower and upper quartile of normal Distribution.
• Define Degree of freedom.
• Define confidence interval.
• Differentiate between software and hardware.
• What are the output devices in the computer?

Q3

• Explain the sample Proportion.
• What is meant by Bias?
• Elaborate the term Statistic.
• Define Target Population.
• Describe the term simple random sample.
• Explain sampling Distribution.
• Define Regression.
• What is meant by Scatter Diagram?
• Elaborate the term Residual.
• Write down four properties of correlation coefficient.
• Intercept the meaning of r = 0
• Define perfect positive correlation.

Q.4

• what is meant by Attribute?
• What do you understand by Association?
• Define Cyclical Movements?
• Define moving average Method.
• The given values represent the 3- year Moving Total 168,177,189,201,207,216 Compute the 3-year Moving average.
• Given the trend equation ŷ = 80 + 2.5x with origin 2004 and yearly data given from
• 2004 to 2010 find the estimated value for 2008.
• Given ∑d2  = 440 and n = 11, find the value of rs.
• Given ∑x –∑x3 = 0 , ∑x2= 70, ∑xy = 140 Determine the value of “b”.
• Define Irregular Variations in the Time series.

Section-II

Q.5
(a)In a normal Distribution µ = 20 and σ = 5 find the two point containing middle 95%
area between them.

(b).X is N (100, 64) find: (i) P (90≤x≤115) (ii) P (x≥ 110)

Q.6
(a) Draw all possible samples of size 2 with replacement from the population 2,4,6,8  
show that σ2 =
(b)The random variable “X” has the following probability Distribution

Find S.E () for a random sample of 25

Q.7
(a) Calculate 95% confidence Interval for population Mean, Given that σ2 = 49, n = 25,  
 = 83.0 (4)

(b)A basket ball player has hit on 60% of his shots from the floor, If on the next 100
shots he makes 70 baskets, would you say that his shoting has improved. α = 5%

Q.8
(a) Fit Least Squares line to the following data.

        
Also find trend values for each value of x and show that ∑ (y – ŷ) = 0

(b)From the following data compute coefficient of correlation:
N = 10,  = 14.6,  = 12.7, ∑(x-)2 = 115.96, ∑(y-)2 = 59.04, ∑(x-)(y-) = 53.95

Q.9
(a) Can vaccine be regarded as preventive measure for small pox from the following 
data: of 1482 person in a locality exposed to small pox, 368 in all wer attacked. Of
1482 persons 343 persons had been vaccinated and of these 35 were attacked.

(b)Given the Parabola ŷ = 10.4 + 0.6x + 0.7x2 with origin at 1980 and unit of
Measurement for x is one year shift the origin to 1975.

Attempt any three Parts
Section – III    (Practical Part)

Q.10
(a) A population has the values as 1,2,4 take all possible samples of size 2 with
replacement and verify that: (i) µ = µ    (ii) σ2 =  2
(b)Given that n1 = 40 , 1 = 15, s1 = 8. Test the Hypothesis that Mean in the population
is 16.
(c) Given the following data. Find the regression equation of x on y.

(d)Test the Association between two attribute A and B.

(e)Given the following Time series Find out Trend values by the method of Least squares
by fitting a Straight Line.