# Statistical Methods-Non-Parametric Test (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 12 - 14 of 16

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## Question number: 12

» 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

## Question number: 13

» 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.

## Question number: 14

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2011

### Describe in Detail

Let the temperature before and after administration of aspirin be

Patient | Before | After |

1 | 100.0 | 98.1 |

2 | 102.1 | 97.2 |

3 | 100.6 | 98.6 |

4 | 100.1 | 99.1 |

5 | 101.5 | 97.6 |

6 | 102 | 98.6 |

7 | 99.9 | 98.2 |

8 | 102.7 | 98.1 |

9 | 100.40 | 98.2 |

10 | 100.8 | 97.1 |

Test by the sign test; whether aspirin is effective in reducing temperature. What is the p-value of the calculated statistic?

### Explanation

Let M _{1} and M _{2} is the median temperature of the patients. The hypothesis for test is

Fir this first find the difference of median

Also find the difference of temperature of before and after

d _{i} 2.1 4.9 2.0 1.0 3.9 3.4 1.7 4.6 2.4 3.7