# ISS (Statistical Services) Statistics Paper IV: Questions 12 - 15 of 79

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## Question number: 12

» Statistical Quality Control » Acceptance Sampling by Attributes

### Describe in Detail

What is Type –I Error? What is type-II error? What is probability of rejecting a lot which contains acceptable quality level known as?

### Explanation

Type I error— rejecting a lot that is good.

When the null hypothesis is true and we reject it, it is known as type I error.

Producer’s risk is the probability of rejecting a good lot considering it as a bad lot by the consumer. Hence, Producer’s Risk is also known as Type I error.

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## Question number: 13

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Six samples, which contain 20 observations per sample, have been collected and the sample means and sample ranges are computed as shown below. Test whether the sample means are within control limits for ?

Sample | Mean | Range |

1 | 3.06 | 0.42 |

2 | 3.15 | 0.5 |

3 | 3.11 | 0.41 |

4 | 3.13 | 0.46 |

5 | 3.06 | 0.46 |

6 | 3.09 | 0.45 |

### Explanation

The sample size here is 20.

We are given that

Sample | Mean ( | Range (R) |

1 | 3.06 | 0.42 |

2 | 3.15 | 0.5 |

3 | 3.11 | 0.41 |

4 | 3.13 | 0.46 |

5 | 3.06 | 0.46 |

6 | 3.09 | 0.45 |

… (48 more words) …

## Question number: 14

» Statistical Quality Control » Control Charts » Variable

### Describe in Detail

Construct a control chart for mean for the following data based on fuses, samples of 5 being taken every hour. Check whether the production is under control?

Sample No. | Observations | |||||

1 | 42 | 65 | 75 | 78 | 87 | 87 |

2 | 42 | 45 | 68 | 72 | 90 | 90 |

3 | 19 | 24 | 80 | 81 | 81 | 81 |

4 | 36 | 54 | 69 | 77 | 84 | 84 |

5 | 42 | 51 | 57 | 59 | 78 | 78 |

6 | 51 | 74 | 75 | 78 | 132 | 132 |

7 | 60 | 60 | 72 | 95 | 138 | 138 |

8 | 18 | 20 | 27 | 42 | 60 | 60 |

9 | 15 | 30 | 39 | 62 | 84 | 84 |

10 | 69 | 109 | 113 | 118 | 153 | 153 |

11 | 64 | 90 | 93 | 109 | 112 | 112 |

12 | 61 | 78 | 94 | 109 | 136 | 136 |

Total | 859.2 | 716 |

### Explanation

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

1 | 42 | 65 | 75 | 78 | 87 | 87 | 347 | 69.4 | 45 |

2 | 42 | 45 | 68 | 72 | 90 | 90 | 317 | 63.4 | 48 |

3 | 19 | 24 | 80 | 81 | 81 | 81 | 285 | 57.0 | 62 |

4 | 36 | 54 | 69 | 77 | 84 | 84 | 320 | 64.0 | 48 |

5 | 42 | 51 | 57 | 59 | 78 | 78 | 287 | 57.4 | 36 |

6 | 51 | 74 | 75 | 78 | 132 | 132 | 410 | 82.0 | 81 |

7 | 60 | 60 | 72 | 95 | 138 | 138 | 425 | 85.0 | 78 |

8 | 18 | 20 | 27 | 42 | 60 | 60 | 167 | 33.4 | 42 |

9 | 15 | 30 | 39 | 62 | 84 | 84 | 230 | 46.0 | 69 |

10 | 69 | 109 | 113 | 118 | 153 | 153 | 562 | 112.4 | 84 |

11 | 64 | 90 | 93 | 109 | 112 | 112 | 468 | 93.6 | 48 |

12 | 61 | 78 | 94 | 109 | 136 | 136 | 478 | 95.6 | 75 |

Total | 859.2 | 716 |

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## Question number: 15

» Statistical Quality Control » Acceptance Sampling by Attributes

### Describe in Detail

a) What is the small percentage of defects that consumers are willing to accept?

b) What is upper limit of the percentage of defective items consumers are willing to tolerate?

c) What is probability that a lot will be accepted that contains a greater number of defects than the LTPD limit known as?

### Explanation

a) The small percentage of defects that consumers are willing to accept is known as Acceptance Quality level (AQL).

If is a lot with relatively small fraction defective, that we do not wish to reject then

P (rejecting a lot of quality ) = 0.05 Or P (Accepting a lot of quality ) = 0.95

Consumers are willing to accept this small percentage o

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