# 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

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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)beforetraining 10.6 10.9 10.1 10.5 11 11.2 10.7 10.2 10.9 10.6 Time (in sec)aftertraining 10.1 10.7 9.9 10 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

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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. 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)

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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

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

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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.

First find the cdf of Y

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