Question bank

1. NBA ACCREDITED
DEPARTMENT OF MATHEMATICS
QUESTION BANK
SUBJECT CODE NAME: 18CBME41/18CBAE41/11CBME41
STATISTICS AND NUMERICAL METHODS (SNM)
SEMESTER / YEAR : IV / II B.E MECH/AUTO
UNIT I
TESTING OF HYPOTHESIS
PART A Marks : 10x1=10
1. In testing of hypothesis, small sample test must be
a) Less than “30”
b) Greater than or Equal to “30”
c) Less than “100”
d) Greater than or Equal to “100”
2. “In hypothesis testing, a Type 2 error” occurs when
a) The null hypothesis is not rejected when the null hypothesis is true.
b) The null hypothesis is rejected when the null hypothesis is true.
c) The null hypothesis is not rejected when the alternative hypothesis is true.
d) The null hypothesis is rejected when the alternative hypothesis is true.

2. 3. Null and alternative hypotheses are statements about:
a) population parameters.
b) sample parameters.
c) sample statistics.
d) it depends - sometimes population parameters and sometimes sample statistics.
4. Which of the following is NOT true about the standard error of a statistic?
a) The standard error measures, roughly, the average difference between the statistic and the
population parameter.
b) The standard error is the estimated standard deviation of the sampling distribution for the
statistic.
c) The standard error can never be a negative number.
d) The standard error increases as the sample size(s) increases.
5. A hypothesis test is done in which the alternative hypothesis is that more than 10% of a
population is left-handed. The p-value for the test is calculated to be 0.25. Which statement
is correct?
a) We can conclude that more than 10% of the population is left-handed.
b) We can conclude that more than 25% of the population is left-handed.
c) We can conclude that exactly 25% of the population is left-handed.
d) We cannot conclude that more than 10% of the population is left-handed.
6. A result is called “statistically significant” whenever
a) The null hypothesis is true.
b) The alternative hypothesis is true.
c) The p-value is less or equal to the significance level.
d) The p-value is larger than the significance level.
7. The confidence level for a confidence interval for a mean is
a) the probability the procedure provides an interval that covers the sample mean.
b) the probability of making a Type 1 error if the interval is used to test a null hypothesis
about the population mean.
c) the probability that individuals in the population have values that fall into the interval.
d) the probability the procedure provides an interval that covers the population mean.
8. Which of the following is not a correct way to state a null hypothesis?

3. a)𝐻0 : 𝑝1
̂ - 𝑝2
̂ = 0. (Sample statistics do not go into hypotheses)
b) 𝐻0 :𝜇𝐷 = 10.
c) 𝐻0 :𝜇1 - 𝜇2 = 0.
d) 𝐻0 : p = 0.5.
9. If the word significant is used to describe a result in a news article reporting on a study,
a) the p-value for the test must have been very large.
b) the effect size must have been very large.
c) the sample size must have been very small.
d) it may be significant in the statistical sense, but not in the everyday sense.
10. The average time in years to get an undergraduate degree in computer science was compared
for men and women. Random samples of 100 male computer science majors and 100 female
computer science majors were taken. Choose the appropriate parameter(s) for this situation.
a) One population proportion p.
b) Difference between two population proportions p1 - p2.
c) One population mean 𝜇1.
d) Difference between two population means µ1 - µ2.
PART B Marks : 5x8=40
1. Two samples of sizes 1000 and 2000 are drawn from a normal population with SD 40. The
SD of the first sample was found to 42 and that of the second was found to be 44. Is the
difference significant?
2. A die is thrown 400 times and a throw of 3 or 4 is observed 150 times.
3. Random samples of 400 men and 600 women were asked whether they would
like to have a fly-over near their residence 200 men and 325 women were in
favour of it. Test the equality of proportion of men and women in the proposal
4. A sample analysis of examination results of 1000 students were made and
it was found that 260 failed, 110 first class, 420 second class and rest obtained
third class. Applying Chi-square test whether the general examination result is
in the ratio 2:1:4:3.
5. Random samples of 400 men and 600 women were asked whether they would
like to have a fly-over near their residence 200 men and 325 women were in
favour of it. Test the equality of proportion of men and women in the proposal.

4. UNIT II
CORRELATION AND REGRESSION ANALYSIS
PART A Marks : 10x1=10
1. The coefficient of correlation
a) is the square of the coefficient of determination
b) is the square root of the coefficient of determination
c) is the same as r-square
d) can never be negative
2. The correlation coefficient is the_______of two regression coefficients:
a) Geometric mean
b) Arithmetic mean
c) Harmonic mean
d) Median
3. When two regression coefficients bear same algebraic signs, then correlation coefficient is:
a) Positive
b) Negative
c) According to two signs
d) Zero
4. If the coefficient of determination is a positive value, then the regression equation
a) must have a positive slope
b) must have a negative slope
c) could have either a positive or a negative slope
d) must have a positive y intercept
5. In regression analysis, if the independent variable is measured in kilograms, the dependent
variable
a) must also be in kilograms
b) must be in some unit of weight
c) cannot be in kilograms
d) can be any units
6. If the coefficient of determination is 0.81, the correlation coefficient
a) is 0.6561
b) could be either + 0.9 or - 0.9
c) must be positive
d) must be negative

5. 7. If the coefficient of determination is equal to 1, then the correlation coefficient
a) must also be equal to 1
b) can be either -1 or +1
c) can be any value between -1 to +1
d) must be -1
8. If one regression coefficient is greater than one, then other will he:
a) More than one
b) Equal to one
c) Less than one
d) Equal to minus one
9. If Y = 2 - 0.2X, then the value of Y intercept is equal to:
a) -0.2
b) 2
c) 0.2X
d) All of the above
10. The straight line graph of the linear equation Y = a + bX, slope is horizontal if:
a) b = 0
b) b ≠ 0
c) b = 1
d) a = b
PART B Marks : 5x8=40
1. Calculate the coefficient of correlation between x and y from the following
data.
X 1 3 5 8 9 10
Y 3 4 8 10 12 11

6. 2. Find the rank correlation coefficient for the following data:
x 92 89 87 86 86 77 71 63 53 50
y 86 83 91 77 68 85 52 82 37 57
3. Obtain the least square regression line of y on x for the following data:
x 1 2 3 4 5 6 7 8 9
y 9 8 10 12 11 13 14 16 15
Also obtain an estimate of y which should correspond on an average to x = 6.2.
4. Find the coefficient of correlation between x and y from the following data:
5. Find the rank correlation coefficient between x and y from the following
data:
x 18 78 46 37 47 56 82 47 46
y 46 81 38 44 38 47 75 56 63
x 5 10 5 11 12 4 3 2 7 1
y 1 6 2 8 5 1 4 6 5 2

7. UNIT III
SOLUTION OF EQUATIONS AND EIGEN VALUE PROBLEMS
PART A Marks : 10x1=10
1. The Newton-Raphson method of finding roots of nonlinear equations
falls under the category of _____________ methods.
a) bracketing
b) open
c) random
d) graphical
2. The next iterative value of the root of 𝑥2
- 4 = 0 using the Newton-
Raphson method, if the initial guess is 3, is
a) 1.5
b) 2.067
c) 2.167
d) 3.000
3. Solving an engineering problem requires four steps. In order of sequence
the four steps are
a) formulate, model, solve, implement
b) formulate, solve, model, implement
c) formulate, model, implement, solve
d) model, formulate, implement, solve

8. 4. One of the roots of the equation 𝑥3
- 3 𝑥2
+ x – 3 = 0 is
a) -1
b) 1
c) √3
d) 3
5. The bisection method of finding roots of nonlinear equations falls under
the category of a (an) _________ method.
a) open
b) bracketing
c) random
d) graphical
6. If for a real continuous function f( x), f(a)f(b) < 0, then in the range of
[a,b] for f (x) = 0 , there is (are)
a) one root
b) an undeterminable number of roots
c) no root
d) at least one root
7. The goal of forward elimination steps in the Gauss elimination method is
to reduce the coefficient matrix to a (an) _____________ matrix.
a) diagonal
b) identity
c) lower triangular
d) upper triangular

9. 8. Division by zero during forward elimination steps in Naïve Gaussian
elimination of the set of equations [A][X ] = [C] implies the coefficient
matrix [A]
a) is invertible
b) is nonsingular
c) may be singular or nonsingular
d) is singular
9. The Newton Raphson method is also called as ____________
a) Tangent method
b) Secant method
c) Chord method
d) Diameter method
10.The convergence of which of the following method depends on initial
assumed value?
a) False position
b) Gauss Seidel method
c) Newton Raphson method
d) Euler method
PART B Marks : 5x8=40
1. Find by Newton Raphson method a positive root of the equation
3𝑥 − cos 𝑥 − 1 = 0.Calculate the first approximation in finding
the smallest positive root of 𝑥3
− 3𝑥 + 1 = 0 that lie between 0 and 1.

10. 2. Solve the equations2𝑥 + 𝑦 + 4𝑧 = 12, 8𝑥 − 3𝑦 + 2𝑧 = 20 4𝑥 + 11𝑦 − 𝑧 = 33
by Gauss elimination method.
3. Find an Iterative formula to find √𝑁 where N is a positive integer, using Newton’s
method and hence find √11
4. Using the Bisection method , find the negative root of the equation
𝑥3
− 4𝑥 + 9 = 0
5. Solve by Gauss Jordan method of equation𝑥 + 𝑦 + 𝑧 = 9, 2𝑥 − 3𝑦 + 4𝑧 = 13,
3𝑥 + 4𝑦 + 5𝑧 = 40.
UNIT IV
INTERPOLATION, NUMERICAL DIFFERENTIATION AND NUMERICAL
INTEGRATION
PART A Marks : 10x1=10
1. Given n+1 data pairs, a unique polynomial of degree ______________ passes
through the n 1 data points.
a) n 1
b) n
c) n or less
d) n 1 or less
2. is used to denote the process of finding the values inside the interval(X0, Xn).
a) Interpolation
b) Extrapolation
c) Iterative
d) Polynomial equation
3. Lagrange's interpolation formula is used to compute the values for------
intervals.
a) equal
b) unequal
c) open
d) closed

11. 4. Newton forward interpolation formula is used for------intervals.
a) equal
b) unequal
c) open
d) closed
5. To find the derivative for the start value (lies between) of the table formula is
used.
a) Newton Forward Interpolation Formula
b) Newton Backward Interpolation Formula
c) Newton Forward Difference Formula
d) Newton Backward Difference Formula
6. To find the derivative for the end value (lies between) of the table
formula is used.
a) Newton Forward Interpolation Formula
b) Newton Backward Interpolation Formula
c) Newton Forward Difference Formula
d) Newton Backward Difference Formula
7. Interpolating polynomial is also known as .
a) smoothing function
b) interpolating function
c) collocation polynomial
d) interpolating formula
8. The method used to find the dominant Eigen value is .
a) Gauss Method
b) Newton's Method
c) Euler's Method
d) Power Method
9. The (n+1)th
polynomial of a degree n is .
a) n
b) n+1
c) a constant
d) zero

12. 10. Backward substitution method is applied in .
a) Gauss Elimination Method
b) Gauss Seidal Method
c) Gauss Jacobi Method
d) Newton's Raphson Method
PART B Marks : 5x8=40
1. Find the polynomial 𝑓(𝑥) by using Langrages formula and hence find 𝑓(3) for
X 0 1 2 5
F(x) 2 3 12 147
2. Find yꞌ(x) for given datas and hence find yꞌ(x) at x = 0.5
X 0 1 2 3 4
Y (x) 1 1 15 40 85
3. Find the first derivative of y with respect to x at x= 10 from the data given below
X 3 5 7 9 11
Y 31 43 57 41 27
4. Evaluate ∫
1
1+𝑥2
𝑑𝑥
1
0
using Trapezoidal rule with h = 0.2
5. Using Taylor’s series find y at x=0 if 𝑦′
= 𝑥2
𝑦 − 1 , 𝑦(0) = 1.
UNIT V
NUMERICATL SOLUTIONS OF ORDINARYDIFFERENTIAL EQUATIONS
PART A Marks : 10x1=10
1. Numerical differentiation can be used only when the difference of some order are

13. .
a) equally spaced
b) unequally spaced
c) constant
d) independent
2. In deriving the trapezoidal formula for the curve y=f(x), each sub-interval is replaced by its
.
a) straight line
b) ellipse
c) chord
d) tangent line
3. Simpson's rule will give exact result if the entire curve y=f(x) is itself a
a) straight line
b) ellipse
c) parabola
d) tangent line
4. Taylor's series method will be very useful to give some initial starting values for powerful
methods such as .
a) Euler Method
b) Modified Euler Method
c) Newton Raphson Method
d) Runge Kutta Method
5. The modified Euler method is based on the average of .
a) straight line
b) ellipse
c) chord
d) points
6. The simplest method in finding the approximate solutions to the first order equations is
a) Euler's method
b) Modified Euler's Method
c) Runge-Kutta method
d) Taylor's Method
7. The most popular Runge-Kutta method is .
a) First order Runge-Kutta method
b) Second order Runge-Kutta method
c) Third order Runge-Kutta method
d) Fourth order Runge-Kutta method

14. 8. The process of numerical integration of a function of a single variable is called .
a) Trapezoidal Rule
b) Simpson's Rule
c) Cubature
d) Quadrature
9. Simpson's rule for evaluation of integral gives better result if f(x) = 0 represents .
a) a circle
b) a parabola
c) an ellipse
d) a hyperbola
10. The process of numerical integration of a function of a two variable is called
a) Trapezoidal Rule
b) Simpson'sRule
c) Cubature
d) Quadrature
PART B Marks : 5x8=40
1. Apply modified Euler's method to find 𝑦(0.2) and 𝑦(0.4) given 𝑦 ′ = 𝑥2
+ 𝑦2
,
𝑦(0) = 1 taking h = 0.2.
2. Given 𝑦 ′ = 𝑥𝑦 + 𝑦2
, 𝑦 (0) = 1, use Taylor series method to get the value of
𝑦(0.1), 𝑦(0.2) and 𝑦(0.3).
3. Solve 𝑦 ′ =
1
2
(1 + 𝑥2
)𝑦2
, 𝑦(0) = 1, 𝑦(0.1) = 1.06, 𝑦(0.2) = 1.12, 𝑦(0.3) = 1.21.
Compute 𝑦(0.4), using Milne's Predictor Corrector formula.
4. Evaluate ∫ 𝑥4
𝑑𝑥
3
−3
using Trapezoidal rule and Simpson’s
1
3
𝑟𝑑 rule.
5. Solve 𝑦 ′ = 𝑥 + 𝑦 and 𝑦 (0) = 1 by Taylor series method. Find the value of 𝑦 at 𝑥 = 0.1
and 𝑥 = 0.2.