An industrial engineer tests 4 different shop-floor layouts by having each of 6
ID: 3152605 • Letter: A
Question
An industrial engineer tests 4 different shop-floor layouts by having each of 6 work crews construct a subassembly and measuring the construction times (minutes) as follows:
Layout 1
Layout 2
Layout 3
Layout 4
Crew A
48.2
53.1
51.2
58.6
Crew B
49.5
52.9
50.0
60.1
Crew C
50.7
56.8
49.9
62.4
Crew D
48.6
50.6
47.5
57.5
Crew E
47.1
51.8
49.1
55.3
Crew F
52.4
57.2
53.5
61.7
Test at the 0.01 level of significance whether the 4 floors layouts produce different assembly times and whether some of the work crews are consistently faster in constructing this subassembly than the others.
{please use excel if needed for this problem, and provide steps to what you did to calculate any data found in excel. for everything else, please show all steps. thank you}
Layout 1
Layout 2
Layout 3
Layout 4
Crew A
48.2
53.1
51.2
58.6
Crew B
49.5
52.9
50.0
60.1
Crew C
50.7
56.8
49.9
62.4
Crew D
48.6
50.6
47.5
57.5
Crew E
47.1
51.8
49.1
55.3
Crew F
52.4
57.2
53.5
61.7
Explanation / Answer
Solution:
Here, we have to test whether the 4 floors layouts produce different assembly times and whether some of the work crews are consistently faster in constructing this subassembly than the others. For checking this claim we have to use the one way analysis of variance for finding the significant difference in the assembly times for given four floors layouts. The null and alternative hypothesis is given as below:
Null hypothesis: H0: There is no any significant difference in the average assembly times for four floors layouts.
Alternative hypothesis: Ha: There is a significant difference in the average assembly times for the four floors layouts.
We assume the level of significance for this test as alpha = 0.05.
The ANOVA table for this test is given as below:
Descriptives
Construction time
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
Layout 1
6
49.4167
1.90096
.77607
47.4217
51.4116
47.10
52.40
Layout 2
6
53.7333
2.68601
1.09656
50.9145
56.5521
50.60
57.20
Layout 3
6
50.2000
2.02583
.82704
48.0740
52.3260
47.50
53.50
Layout 4
6
59.2667
2.67333
1.09138
56.4612
62.0721
55.30
62.40
Total
24
53.1542
4.53374
.92545
51.2397
55.0686
47.10
62.40
ANOVA
Construction time
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
362.365
3
120.788
21.883
.000
Within Groups
110.395
20
5.520
Total
472.760
23
For this ANOVA test, we get the p-value as 0.00 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that There is no any significant difference in the average assembly times for four floors layouts.
This means, There is a significant difference in the average assembly times for four floors layouts.
Descriptives
Construction time
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
Layout 1
6
49.4167
1.90096
.77607
47.4217
51.4116
47.10
52.40
Layout 2
6
53.7333
2.68601
1.09656
50.9145
56.5521
50.60
57.20
Layout 3
6
50.2000
2.02583
.82704
48.0740
52.3260
47.50
53.50
Layout 4
6
59.2667
2.67333
1.09138
56.4612
62.0721
55.30
62.40
Total
24
53.1542
4.53374
.92545
51.2397
55.0686
47.10
62.40