# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 55 - 60 of 72

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## Question number: 55

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2010

### Describe in Detail

Let (X, Y) be jointly distributed with density function

Obtain correlation coefficient between X and Y

### Explanation

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## Question number: 56

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2011

### Describe in Detail

Let the temperature before and after administration of aspirin be

Patient | Before | After |

1 | 100·0 | 98·1 |

2 | 102·1 | 97·2 |

3 | 100·6 | 98·6 |

4 | 100·1 | 99·1 |

5 | 101·5 | 97·6 |

6 | 102 | 98·6 |

7 | 99·9 | 98·2 |

8 | 102·7 | 98·1 |

9 | 100.40 | 98·2 |

10 | 100·8 | 97.1 |

Test by the sign test; whether aspirin is effective in reducing temperature. What is the p-value of the calculated statistic?

### Explanation

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## Question number: 57

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2010

### Describe in Detail

Show that for discrete distribution β _{2} > 1

### Explanation

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## Question number: 58

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2010

### Describe in Detail

How large a sample must be taken in order that the probability will be at least 0·95 that X _{n} will be within 0·5 of µ (µ is unknown and σ = l).

### Explanation

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## Question number: 59

» Statistical Methods » Measures of Location

Appeared in Year: 2013

### Describe in Detail

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

### Explanation

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## Question number: 60

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2015

### Describe in Detail

Let X _{1}, X _{2}, …, X _{12} be a random sample from a normal N (µ _{1}, σ _{1}^{2}) and Y _{1}, Y _{2}, …Y _{10} be another random sample from normal N (µ _{2}, σ _{2}^{2}), independently to each other. Carry out an appropriate test for testing

at 5 % level of significance. It is given that .

### Explanation

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