3. A company was concerned about the increasing number of defects and went to th
ID: 3289306 • Letter: 3
Question
3. A company was concerned about the increasing number of defects and went to their training staff and had them develop a training program to reinforce the proper way to assemble the gearmotors. The training program was given to the first shift but not the second shift. You are given the defects per operato The number of monthly defects per operator was taken for the month before the training and the month after the training Statistics were gathered from the shift who was training as well as the shift that was not trained. Did the training significantly reduce the number of defects? A. Write out the null and alternative hypotheses and interpret your results in terms of the hyptheses B. Perform the correct statistical test C. Highlight the result you use to interpret the test and report in words your conclusion about the hypothesis In addition you are to make specific recommendations to the training staff with regard to the future of the training program they developed. You are to be professional in what you report and recommend to the training staff. There is an extra step to this one- think carefully before running the stat test- You can find information in one of the MyMedia presentations First shift defects Operato Before After Second shift defects Operator Before After 4 4 4 17 4 4 20 21 23 24 12Explanation / Answer
Solution:-
Assume that ?1 = Population mean difference (before - after) defect per employee on 1st shift & ?2 = Population mean difference (before - after) defect per employee on the 2nd shift & that ?1, ?2 ~ Normal distribution.
H0: ?1 = ?2
H1: ?1 > ?2 (then after only we would inter the training had some +ve effect)
1st shift defects
2nd shift defects
Operator
Before
After
Difference
Operator
Before
After
Difference
1
3
2
1
13
6
5
1
2
4
0
4
14
7
6
1
3
2
0
2
15
3
5
-2
4
1
1
0
16
4
3
1
5
0
0
0
17
2
4
-2
6
2
3
-1
18
5
3
2
7
3
1
2
19
4
2
2
8
2
1
1
20
2
1
1
9
2
1
1
21
2
1
1
10
1
0
1
22
6
3
3
11
0
0
0
23
3
2
1
12
5
1
4
24
1
2
-1
x1bar
1.25
x2bar
0.667
s1
1.54
s2
1.557
Test Statistic = (x1bar - x2bar) / sort (s12/12 + s22/12) = (1.25 - 0.667) /
Sort ((1.542+1.5572)/12) = 0.922
At 95% confidence level, Z = NORM.INV (95%, 0, 1) = 1.64
So that Test Statistic is less than Z, we fail to reject the theorem, & infer that ?1 = ?2 i.e. the training was ineffective.
1st shift defects
2nd shift defects
Operator
Before
After
Difference
Operator
Before
After
Difference
1
3
2
1
13
6
5
1
2
4
0
4
14
7
6
1
3
2
0
2
15
3
5
-2
4
1
1
0
16
4
3
1
5
0
0
0
17
2
4
-2
6
2
3
-1
18
5
3
2
7
3
1
2
19
4
2
2
8
2
1
1
20
2
1
1
9
2
1
1
21
2
1
1
10
1
0
1
22
6
3
3
11
0
0
0
23
3
2
1
12
5
1
4
24
1
2
-1
x1bar
1.25
x2bar
0.667
s1
1.54
s2
1.557
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