# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 13 - 18 of 72

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## Question number: 13

» Statistical Methods » Measures of Location

Appeared in Year: 2010

### Describe in Detail

Let F _{n} (x) be the distribution function define by

Is the lim F _{n} (x) a distribution function? If not, why?

### Explanation

The function F _{n} (x) is a distribution function if

By the definition , but here this is not equal to one. This says that F _{n} (x) is not a distribution function.

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## Question number: 14

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2013

### Describe in Detail

For a trivariate population, it is given that:

σ _{1} =3, σ _{2} =4, σ _{3} =5, r _{12} =0.7, r _{13} =0.6, r _{23} =0.4

Compute all partial and multiple correlation coefficients.

### Explanation

Given that there are three variable X _{1}, X _{2}, X _{3} for a trivariate population. The partial correlation coefficient is between any two variable eliminating the third variable. So, the parital correlation between X _{1} and X _{2} is

the parital correlation between

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## Question number: 15

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2014

### Describe in Detail

Define power of a test and discuss its role in selecting the best test. Describe a test procedure for testing equality of means of two independent normal populations, when standard deviations are equal but unknown for small samples.

### Explanation

** Power of a test: ** The power function is the probability of rejection the null hypothesis when the alternative hypothesis is true. In statistical terms,

The quantity 1-β is called the power of the test. So, the power of the test is depends upon the difference between the parameter values specified in H _{0} and actual value of th

… (157 more words) …

## Question number: 16

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2012

### Describe in Detail

Define partial correlation coefficient r _{12.3 } between x _{1} and x _{2} eliminating from each the effect of x _{3}. Derive the expression for r _{12.3 } and comment on its usefulness in multivariate data analysis.

### Explanation

Partial correlation coefficient defined as a association between any two variables out of a set of eliminating the other variable. Consider three variables X _{1}, X _{2} and X _{3}. Now we want to find out the partial correlation coefficient r _{12.3 } between X _{1} and X _{2} eliminating the linear effect of X _{3} on X _{1} and X _{2}. In this situation, define two res

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## Question number: 17

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2009

### Describe in Detail

Ten experts have given scores of effectiveness on two teams A and B as given below.

Expert | Score on A | Score on B |

1 | 7 | 9 |

2 | 4 | 5 |

3 | 8 | 8 |

4 | 9 | 8 |

5 | 3 | 6 |

6 | 6 | 10 |

7 | 8 | 9 |

8 | 10 | 8 |

9 | 9 | 4 |

10 | 5 | 9 |

Are the distribution of scores for group A above that of group B?

### Explanation

Let n _{1} be the number of scores of effectiveness on team A with median score m _{1}, and n _{2} the number of scores of effectiveness on team B with median score m _{2}. Then the hypothesis is that the median score of the two teams are same against the alternative that they are not same.

For this first arrange the observations of the

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## Question number: 18

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2015

### Describe in Detail

Let (X, Y) be distributed as bivariate normal BVN (3,1, 16,25,3/5). Calculate P (4 < Y < 11.84|X=7)

### Explanation

We had known that the conditional distribution of Y given X has mean and variance .

Using conditional mean and variance

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