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

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## Question number: 12

Essay Question▾

### 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

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## Question number: 13

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### 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 (Equation Range (R) 1 3.06 0.42 2
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## Question number: 14

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### 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 (Equation ) 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
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## Question number: 15

Essay Question▾

### 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

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