# Statistical Methods-Non-Parametric Test (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 15 - 16 of 16

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## Question number: 15

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2015

### Describe in Detail

Given the random samples

X: 1,5, 7,9, 15,17,21,23

Y: 2,6, 10,12,18,20,26,28,32

From the populations having the distribution function respectively as F _{1} and F _{2}, test the hypothesis

against

at 5 % level of significance by the Wald-Wolfowitz run test. It is given that the critical number of runs at the sample sizes (8,9) at 5 % level is 5.

### Explanation

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 8 and sample 2 is Y variables of size m = 9 from two population F _{1} (x) and F _{2} (y) respectively.

The hypothesis under the test is that the null hypothesis is the two population are identical otherwise the alternative is the population is differ.

… (96 more words) …

## Question number: 16

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2009

### Describe in Detail

Given the following data:

x | 0 | 1 | 3 |

f (x) | 1 | 3 | 55 |

find a polynomial P (x) of degree 2 or less so that P (x) = f (x) at the tabulated values of x. Hence

approximate f (2).

### Explanation

Let the a polynomial is P (X) = kx ^{2} +lx + m, where k, l, m are constants which is determine by using Lagrange’s interpolation polynomial because the x values is not equal interval.

where

x _{0} =0, x _{1} =1 _{, }, x _{2} =3 and f (x _{0}) =1, f (x _{1}) =3, f

… (112 more words) …