# Statistical Methods-Non-Parametric Test (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 7 - 11 of 16

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## Question number: 7

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

Appeared in Year: 2014

### Describe in Detail

Consider two samples as follows:

Sample 1: 1, 4, 7, 9, 16, 17, 22, 24

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

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test. [Given value of Z for α = 0.05 = 1.645, where Z is N (0, 1) ]

### Explanation

Let the sample 1 consider the population X and sample 2 consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample:

## Question number: 8

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2010

### Describe in Detail

The following data represent lifetimes (hours) of batteries for two different brands:

Brand A | 40 | 30 | 40 | 45 | 55 | 30 |

Brand B: | 50 | 50 | 45 | 55 | 60 | 40 |

Test whether two brands are the same.

### Explanation

we use Wilcoxon two-sample test to the following data

Let n _{1} be the number of breakdown times in the Brand A with median time m _{1}, and n _{2} the number of breakdown times in the Brand B with median time m _{2}. Then the hypothesis is

## Question number: 9

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

### Describe in Detail

In a ticket counter, at some point of time the sequence of males (M) and females (F) was found as

MMFMFFFMFMMFFFFMFMMMM

Use runs test to examine if the sequence is random (5 % critical value of the number r of runs with n _{1 } = 11, n _{2 } = 10 is 6).

### 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: 10

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

### Describe in Detail

Apply the Wilcoxon two-sample test to the following data on the first breakdown times of two brands of computers:

Brand A 98, 102, 47, 85, 99, 140, 130

Brand B 95, 125, 160, 155, 148.

Use 1.96 as the critical point for the appropriate test.

### Explanation

Let n _{1} be the number of breakdown times in the Brand A with median time m _{1}, and n _{2} the number of breakdown times in the Brand B with median time m _{2}. Then the hypothesis is that the median times of the two brands are

## Question number: 11

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

Appeared in Year: 2015

### Describe in Detail

Consider the two samples as follows:

Sample I = 6, 7, 8, 10, 12, 14, 16, 23

Sample II: 9, 11, 13, 15, 17, 18, 19, 20, 24

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test at 10 % level of significance. [You can use normal approximation]

### Explanation

Let the sample I consider the population X and sample II consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: