# ISS (Statistical Services) Statistics Paper IV: Questions 43 - 48 of 79

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## Question number: 43

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Following data gives the diameter of the rings manufactured by a company. Obtain the Control limits for R-chart.

Sample No. | Observations | ||||

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 |

4 | 5.03 | 4.91 | 5.01 | 4.98 | 4.89 |

5 | 4.95 | 4.92 | 5.03 | 5.05 | 5.01 |

6 | 4.97 | 5.06 | 5.06 | 4.96 | 5.03 |

7 | 5.05 | 5.01 | 5.10 | 4.96 | 4.99 |

8 | 5.09 | 5.10 | 5.00 | 4.99 | 5.08 |

9 | 5.14 | 5.10 | 4.99 | 5.08 | 5.09 |

10 | 5.01 | 4.98 | 5.08 | 5.07 | 4.99 |

### Explanation

Sample No. | Observations | Total | Sample Mean | Range | ||||

1 | 5.02 | 5.01 | 4.94 | 4.99 | 4.96 | 24.92 | 4.98 | 0.08 |

2 | 5.01 | 5.03 | 5.07 | 4.95 | 4.96 | 25.02 | 5.00 | 0.12 |

3 | 4.99 | 5.00 | 4.93 | 4.92 | 4.99 | 24.83 | 4.97 |

## Question number: 44

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2013

### Describe in Detail

For a PBIB design with parameters**, **b, r, k**, ****, **show that

### Explanation

A PBIB design with m associate classes based on the association scheme is an arrangement of treatments into b blocks such that

(i) Each block contains k distinct treatments (k <

(ii) Each treatment occurs in r blocks

(iii) Any two treatments, which are ith associates

## Question number: 45

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2012

### Describe in Detail

Discus symmetrical BIBD. For an SBIBD, under usual notations, show that

=

### Explanation

**Symmetrical BIBD**:

A BIBD is said to be symmetric if b = υ and r = k.

υ, r, b, k and λ are called the parameters of the BIBD

υ= number of varities or treatments

b = number of blocks

r = number of replicates for each treatment

## Question number: 46

» Design and Analysis of Experiments » Randomized Block and Latin Square Design

Appeared in Year: 2015

### Describe in Detail

Discuss how you would proceed with the analysis if data on one plot is missing in a Latin Square design.

### Explanation

To analysis the data of a Latin square design having missing values, we first estimate the missing value by minimizing the error mean square and the rest missing values by guess estimate which is generally the mean of all available values. The estimated value of x is obtain by to

## Question number: 47

» Design and Analysis of Experiments » Analysis and Layout of Completely Randomized Design

Appeared in Year: 2011

### Write in Short

Explain Randomized block design.

## Question number: 48

» Design and Analysis of Experiments » Basic Principle of Experimental Design

Appeared in Year: 2015

### Describe in Detail

Explain briefly the main principles of design of experiment and analogy in sample surveys with the corresponding concepts.

### Explanation

The main principle of design of experiment is to study the sampling error. If these principles hold, the chance of getting a data set or a design which could be analyzed, with less doubt about structural nuisances, is higher as if the data was collected arbitrarily.

__Principle 1: Fisher’s Principle__