# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 115 - 118 of 165

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## Question number: 115

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2012

### 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 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 and represent the median time of all runner pu

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## Question number: 116

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2013

### 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. If the observed number of runs in a sample lies in between these critical values, the

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## Question number: 117

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

Appeared in Year: 2011

### 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

where , n = 5

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

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

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## Question number: 118

» Probability » Standard Probability Distributions » Lognormal

Appeared in Year: 2015

### 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.

First find the cdf of Y

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