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 typeII 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
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 
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 
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