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

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to **165** questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 550.00 or

## 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.

… (0 more words) …

## 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 X _{1} and X _{3} is

the parital correlation between X _{2} and X _{3} is

The multip…

… (56 more words) …

## 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 specified in H _{0} and actual value of the parameter.

When…

… (135 more words) …

## 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

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

The generating function is

…… (11 more words) …

## 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} eliminating the linear effect of X _{3} on X _{1} and X _{2}. In this situation, define two res…

… (104 more words) …

## 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 same against the alternative that they are not same.

For this first arrange the observations of the combined samples (…

… (119 more words) …