# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 19 - 24 of 165

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## Question number: 19

» 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.

## Question number: 20

» 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

## Question number: 21

» 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

## Question number: 22

» Probability » Probability Generating Functions

Appeared in Year: 2013

### Describe in Detail

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p _{n}, n = 0, I, 2, …… Find the generating function of (i) Pr [X > n],

(ii) Pr [X < n] and (iii) Pr [X = 2n].

### Explanation

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p _{n}. Then

(i) The generating function of Pr [X > n] is denoted by P (z _{ > n})

The generating function is

## Question number: 23

» 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}

## Question number: 24

» 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