# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 23 - 27 of 164

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## Question 23

Appeared in Year: *2012*

### Describe in Detail

Essay▾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 residual var…

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## Question 24

Appeared in Year: *2009*

### Describe in Detail

Essay▾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 (n_{1} + n_{2})…

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## Question 25

Appeared in Year: *2015*

### Describe in Detail

Essay▾Let (X, Y) be distributed as bivariate normal BVN (3, 1,16, 25, ) . 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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## Question 26

Appeared in Year: *2009*

### Describe in Detail

Essay▾A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0·5 at 5 % level of significance?

### Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H_{0}: P = 0.05 against H_{1}: P < 0.05

Here n = 300, numbers of defectives is 10 and

The estimated value of P is

The null hypothesis can be tested by z-test for assuming the sampl…

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## Question 27

Appeared in Year: *2010*

### Describe in Detail

Essay▾You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

Company A | Company B | |

Mean life | 1300 | 1288 |

Standard deviation | 82 | 93 |

Sample size | 100 | 100 |

Which brand of bulbs are you going to purchase if you desire to take a risk of 5 % ?

### Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

The test statistic is

Under H_{0}

The test criteria is reject H_{0} if , otherwise accept it

Here

The tabulated value of t-test is

The …

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