ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 115 - 119 of 165

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Question number: 115

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Ten short-distance runners were put to a rigorous training for two months. Times taken by them to clear 100 metres before and after the training were as follows:

Sl. no. of runner

1

2

3

4

5

6

7

8

9

10

Time (in sec)

before

training

10.6

10.9

10.1

10.5

11.0

11.2

10.7

10.2

10.9

10.6

Time (in sec)

after

training

10.1

10.7

9.9

10.0

11.1

10.9

10.6

10.3

10.5

10.8

Use Wilcoxon’s paired sample signed rank test to examine at 1 % level if the training was at all effective. (The critical value of Wilcoxon’s statistic at 1 % level of significance for n = 10 is 5)

Explanation

In Wilcoxon’s paired sample signed rank test, the null hypothesis that we are sampling two continuous symmetric populations with Equation for the paired-sample case, we rank the differences of the paired observations without regard to sign and proceed as in the single-sample case

Let Equation and Equation represent the median… (203 more words) …

Question number: 116

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Describe the run test for randomness. For the sequence of outcomes of 14 tosses of a coin,

HTTHHHTHTTHHTH, .

test whether the outcomes are in random order. (Given the lower and upper critical values R L = 3,

R u = 12 at 0.05 significance level. )

Explanation

Suppose a sample size n contains n 1 symbols of one type and n 2 symbols of the other type. The null hypothesis is the symbols occur in random order, the alternative is the symbols occur in a set pattern. The lower and upper critical value is obtained from tables.… (99 more words) …

Question number: 117

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x 2) -1 from 0 to 1.

Explanation

T he rule of the integrand using Simpson’s rule for five ordinates is

Equation

where Equation, n = 5

h= (1 - 0) /5 = 1/5

We divide the range 0 to 1 in five equal part i. e.

Equation

Equation

Equation

Equation

Equation

Use Simpson’s rule

Equation

Equation<span class="more">… (1 more words) …</span>

Question number: 118

» Probability » Standard Probability Distributions » Lognormal

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X follow log-normal with parameters µ and σ 2. Find the distribution of Y = aX b, a > 0, -∞ < b < ∞

Explanation

If X follow log-normal with parameters µ and σ 2, then Z = logX follow normal distribution.

Equation

Equation

First find the cdf of Y

Equation

Equation

Equation

Equation

Let Equation

The upper limit is c= Equation, lower limit is Equation

Equation

Equation

Putting the value of c… (8 more words) …

Question number: 119

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2012

Essay Question▾

Describe in Detail

An unknown function u x has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u 3:

x

0

2

5

10

u x

3

19

73

223

Explanation

The Newton’s divided difference formula is used when the x-values not equally spaced. The Newton’s formula of divided difference for estimating u x corresponding to x is

Equation

where Equation, Equation, …

x

y

Equation

Equation

Equation

0

3

8

2

-0.05

2

19

18

1.5

-

5… (21 more words) …

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