# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 70 - 72 of 72

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## Question number: 70

» 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 (x _{2}) =55

The polynomial is

For f (2), the value is

at x = 2

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## Question number: 71

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2009

### Describe in Detail

Explain the method of testing normality by using chi-squared test.

### Explanation

Let X is a random variable follows normal distribution with mean µ and variance σ ^{2}. The testing of null hypothesis is that the population variance σ ^{2} equals a specified value against one of the usual alternatives σ ^{2} < , σ ^{2} > , or σ ^{2} . The appropriate statistic on which to base our decision is the chi-squared statistic.

In chi square stati…

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## Question number: 72

» Statistical Methods » Association and Contingency

Appeared in Year: 2015

### Describe in Detail

Compute Yule’s coefficient of association (Q) and Yule’s coefficient of colligation (Y) for the following table:

Disease on-set | |||

Yes | No | ||

Medicine used | A | 19 | 587 |

B | 193 | 2741 |

### Explanation

The frequencies for various attributes be show in this contingency table

Medicine used | Yes (A) | No (a) |

A (B) | (AB) | (aB) |

B (b) | (Ab) | (ab) |

(i) Yule’s coefficient of association is a relative measure of association between two attributes, for this question the attributes are No-TB and treatment. If (AB), (aB), (Ab)…

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