Assignment 1
Confidence Intervals
1. You want to know the average time to fill a customer order (time from receipt of order to pack and ship order). 10 orders, randomly selected, had an average time of 72.6 hrs and a standard deviation of 6.2 hrs. What is the 95% confidence interval for the mean and standard deviation?
2. An inspector randomly selects 100 parts for an end-of-line audit prior to packing, and finds 5 defective parts. What is the true proportion of good parts produced with 95% certainty?
Assignment 2
Correlation and Regression
Complete the following problems and attach results.
1. P. The Regional Sales Manager has asked you to determine if there is a relationship between the number of sales calls and sales dollars. Perform a correlation and regression analysis, and report your findings.
Assignment 3
Hypothesis Statement
Write the appropriate hypothesis test
1. Data has been collected on fill rate (% line items shipped on-time out of total line items ordered) for its two distribution centers. We want to know if there is a difference between the fill rate of the two distribution centers.
2. A new packing material is being considered for the distribution center. Currently Kleenex is being utilized to wrap products and keep them from touching. The packing material alternative is an ultra soft toilet paper. A test will be run to determine if ultra soft toilet paper will be effective at reducing breakage. The toilet paper will only be implemented if it reduces breakage.
3. Jane, the clinical trial manager, is looking at implementing a new process to reduce the cycle time of field reports. The new process will only be implemented if the reporting time goes down.
4. Your company is looking at a new software system that is supposed to increase the number of claims that can be processed per account manager. The new system will only be purchased if we can increase the number of claims that can be processed. A test will be done to compare the results from both systems.
Assignment 4
Hypothesis Tests for Attribute Data
Complete the following exercises and provide results/output.
1. Data has been collected on fill rate (% items shipped on-time out of total items ordered) for your two distribution centers. 50 orders were randomly selected from each center; 44 items from distribution center 1 and 42 from distribution center 2 were shipped on-time. Is there a difference between the fill rate of the two distribution centers?
2. You want to know if there is a difference in performance of your production lines. A random sample is selected from each line and the number of defects is counted. What is your conclusion?
| Line |
Defects |
Good |
Sample Size |
| 1 |
8 |
292 |
300 |
| 2 |
5 |
295 |
300 |
| 3 |
9 |
291 |
300 |
| 4 |
6 |
294 |
300 |
| 5 |
5 |
295 |
300 |
3. A new packing material is being considered for the distribution center to reduce the breakage of parts. The current material being utilized results in 12% of the parts breaking during shipping. A test is run to determine if the new packing material will be effective at reducing breakage. A sample of 175 parts is reviewed after shipping and 15 are found to be damaged or broken. Should the new packing material be implemented?
Assignment 5
Hypothesis Tests for Means
Complete the following 10 exercises using the appropriate hypothesis test and provide results/output.
Hypothesis Tests for Means - Exercise 1
A customer believes that the product they purchased is high in weight and therefore, is increasing their costs. They send a representative sample of ten products back for testing.
The customer claims the product weights were:
61.3 60.8 61.9 62.2 61.5
60.7 59.9 60.9 61.8 62.0
The products are supposed to be 60.5 kilograms. Does the customer have a legitimate complaint ?
Hypothesis Tests for Means - Exercise 2
A customer believes that the product they purchased is high in weight and therefore, is increasing their costs. They send a representative sample of ten products back for testing.
The customer claims the product weights were:
61.3 60.8 61.9 62.2 61.5
60.7 59.9 60.9 61.8 62.0
Our certified testing facility finds the weights to be:
62.1 61.5 62.3 62.5 61.9
61.0 60.5 61.0 62.0 62.3
Is the customer's test method compatible to the certified testing facility?
Assume the products were tested in the same order, such that 61.3 and 62.1 are the weights for sample 1, etc.
Hypothesis Tests for Means - Exercise 3
The customer service representative decides to call the plant to determine if the product is meeting weight specification today. He asks the Quality Manager for current quality on the two groups that currently produce the product. The Quality Manager sends him the following information:
Gr 14
60.8 60.3 61.0 59.7 60.9
59.9 59.8 60.5 60.1 60.6
Gr 15
60.8 61.2 60.9 60.5 61.1
60.7 61.0 60.9 60.8 60.5
On average, are the two groups producing products with the same weight?
Hypothesis Tests for Means - Exercise 4
In an effort to improve response time, the Information Systems HELP desk just converted to a new system to answer requests for help. Historically, the talk time (the time an agent talks on the phone to a person needing help) has been seven minutes on average. A random sample of ten requests were monitored for talk time to see if the new system had achieved its goal and did indeed have a shorter talk time
The following data was collected during the evaluation period:
5:17 6:45 8:35 7:05 6:55
7:11 5:30 6:03 5:59 6:14
Did the new system achieve its objective?
Hypothesis Tests for Means - Exercise 5
As part of a larger effort to reduce the entire response time when a customer requests special pricing, a new system is being tested to reduce the time to enter a SPA. The new system will be implemented if it reduces the response time by five minutes. The following data was collected:
| Account Manager |
"OLD" System |
Proposed System |
| A |
15.5 |
15.5 |
| B |
19.5 |
15.5 |
| C |
23.0 |
19.0 |
| D |
26.5 |
18.0 |
| E |
20.5 |
15.0 |
| F |
17.0 |
12.5 |
| G |
30.5 |
26.5 |
| H |
5.0 |
5.5 |
| I |
7.5 |
4.0 |
| J |
14.5 |
8.0 |
Should we implement the proposed system ?
Hypothesis Tests for Means - Exercise 6
A glue gun made to dispense 25 ml of glue was calibrated by dispensing 25 ml volumes of glue into ten pre-weighed containers. The actual volumes dispensed were:
25.01 ml, 24.89 ml, 25.10 ml, 24.95 ml, 24.97 ml,
25.04 ml, 25.08 ml, 24.91 ml, 25.07 ml, 24.85 ml
Test the null hypothesis that this glue gun dispenses 25 ml of glue versus the alternate hypothesis that it does not.
Hypothesis Tests for Means - Exercise 7
The hardness of water is measured in terms of the calcium ion concentration (in parts per million). The hardness of the water in hot- and cold-water pipes in a manufacturing process was measured. A technician claims that the hot water is "harder" (has a higher calcium ion concentration) than the cold water. The calcium ion concentrations of the various samples taken are given below:
| Hot Water |
Cold Water |
| 133.5 |
134.0 |
| 135.4 |
134.7 |
| 137.2 |
136.0 |
| 138.4 |
131.7 |
| 136.3 |
134.6 |
| 137.1 |
135.2 |
| 133.3 |
135.9 |
| 136.5 |
135.6 |
| 137.5 |
|
| 139.4 |
|
Test the null hypothesis that the hot and cold water samples have the same calcium ion concentration versus the alternate hypothesis that the hot water has a higher concentration.
Hypothesis Tests for Means - Exercise 8
A chemical plant manufactures paint thinner. The content of ethyl alcohol in the paint thinner is specified as 3ml/liter. To determine if the manufacturing process has shifted above specification, twenty samples of the paint thinner are taken. The volume of ethyl alcohol per liter for each sample is given below:
4.2 5.3 3.5 4.3 3.7 3.2 3.5 2.8 3.5 3.7
2.8 3.3 2.7 3.0 3.1 3.0 3.7 3.3 3.4 2.3
Test the null hypothesis that the process is centered at 3ml/liter ethyl alcohol versus the alternate hypothesis that the mean of the process has shifted to a value greater than 3ml/liter.
Hypothesis Tests for Means - Exercise 9
A manufacturer of fiberglass sheeting implements a new process for reducing the weight of the product. The thickness of the sheeting is an important variable which affects weight. At each of eight thickness, fiberglass sheeting was made with the old and the new process. The weights, in grams, for each combination are given below:
| Thickness |
Old Process |
New Process |
| 1 |
154 |
152 |
| 2 |
159 |
152 |
| 3 |
169 |
171 |
| 4 |
176 |
167 |
| 5 |
183 |
182 |
| 6 |
199 |
194 |
| 7 |
200 |
204 |
| 8 |
213 |
208 |
Test the null hypothesis that there is no difference in fiberglass weight between the old and new process across thickness of sheeting versus the alternate hypothesis that the new process reduces the weight of the fiberglass.
Hypothesis Tests for Means - Exercise 10
Two brands of air filters (A and B) for air conditioning units are tested to determine whether one filter is superior to the other. All filters were tested on the same unit, and the amount of dust (in grams) filtered in 6 hours was measured. The data for both filters is given below:
| Filter A |
Filter B |
| 9.1 |
15.6 |
| 11.8 |
9.3 |
| 1.5 |
16.9 |
| 7.2 |
5.1 |
| 4.2 |
14.5 |
| 9.6 |
19.0 |
| 8.7 |
10.3 |
| 10.2 |
12.5 |
| 4.4 |
13.3 |
|
16.1 |
|
2.6 |
Test the null hypothesis that there is no difference in the average amount of dust filtered by these two filters versus the alternate hypothesis that one filter is better than the other.
Assignment 6
Chi Square Hypothesis Testing
Complete the following exercise and provide results/output.
Your company has three (3) different customer call centers. The Director of Quality suspects that the number of satisfied customers is dependent on the call center, and has asked you to analyze the following data.
|
|
Call Center 1
|
Call Center 2
|
Call Center 3
|
|
Satisfied Customers
|
19
|
21
|
18
|
|
Dissatisfied Customers
|
8
|
3
|
7
|
Is customer satisfaction dependent on the call center?
If so, which call center is different?
Assignment 7
ANOVA
A manufacturer of fiberglass sheeting recently implemented a new process on three (3) machines. The new process reduces the thickness variation of the sheeting; an important variable which affects weight.
As part of the final approval of the new process, you measure the sheet thickness to confirm that there is no difference in the performance of the machines.
What are your results?
What are your conclusions?
Attach output
|
Machine 1
|
Machine 2
|
Machine 3
|
|
0.645
|
0.673
|
0.67
|
|
0.626
|
0.695
|
0.67
|
|
0.685
|
0.671
|
0.627
|
|
0.663
|
0.656
|
0.673
|
|
0.685
|
0.681
|
0.668
|
Assignment 8
Evolutionary Operation
An injecting molding process is producing waste due to flash on the parts. You have been asked to help minimize the waste for this condition. The team decided on the following experimental strategy:
Run 2 2 with center points
Response: waste per hour
Factors: pack pressure and pack time
The normal process range is 7.5-9 for pressure and 5.9-7.5 for time (coded units).
Maximum 5 cycles for Phase I
Statistically significant improvements were found in Phase I however, the optimum was not found so Phase II is run.
Manufacturing process
|
Thickness
|
Temp
|
Cycle Time
|
|
0.254
|
154
|
76
|
|
0.253
|
153
|
75
|
|
0.252
|
152
|
75
|
|
0.251
|
152
|
76
|
|
0.249
|
151
|
77
|
|
0.249
|
151
|
75
|
|
0.248
|
151
|
75
|
|
0.248
|
151
|
80
|
|
0.248
|
151
|
80
|
|
0.247
|
151
|
78
|
|
0.247
|
151
|
80
|
|
0.247
|
151
|
77
|
|
0.247
|
151
|
80
|
|
0.247
|
151
|
76
|
|
0.247
|
151
|
77
|
|
0.246
|
151
|
79
|
|
0.246
|
150
|
76
|
|
0.246
|
150
|
77
|
|
0.246
|
150
|
79
|
|
0.246
|
150
|
78
|
|
0.246
|
150
|
78
|
|
0.245
|
150
|
80
|
|
0.245
|
150
|
79
|
|
0.245
|
150
|
76
|
|
0.245
|
149
|
79
|
Sales data
|
Total Sales (k$)
|
Sales Calls
|
|
102.4
|
175
|
|
103.44
|
122
|
|
109.72
|
135
|
|
89.12
|
77
|
|
91
|
91
|
|
92.24
|
97
|
|
94.84
|
105
|
|
97.32
|
118
|
|
89.64
|
89
|
|
90.4
|
92
|
|
92.64
|
104
|
|
94.64
|
110
|
|
98.4
|
125
|
|
101.32
|
139
|
|
103.84
|
142
|
|
109.24
|
140
|
|
113.32
|
150
|
|
107.1
|
150
|
|
92.4
|
102
|
|
102.8
|
151
|
|
101.04
|
119
|
|
104.2
|
135
|
|
101.4
|
129
|
|
103.92
|
128
|
|
97.32
|
120
|
|
Cycle_Phase I
|
Time_Phase I
|
Pressure_Phase I
|
Waste_Phase I
|
Cycle_Phase II
|
Time_Phase II
|
Pressure_Phase II
|
Waste_Phase II
|
|
1
|
6.7
|
7.5
|
90
|
1
|
5.9
|
8
|
85
|
|
1
|
6.7
|
8
|
86
|
1
|
5.9
|
8.5
|
83
|
|
1
|
6.9
|
7.75
|
90
|
1
|
6.3
|
8.25
|
80
|
|
1
|
7.1
|
7.5
|
98
|
1
|
6.7
|
8
|
83
|
|
1
|
7.1
|
8
|
89
|
1
|
6.7
|
8.5
|
85
|
|
2
|
6.7
|
7.5
|
90
|
2
|
5.9
|
8
|
85
|
|
2
|
6.7
|
8
|
86
|
2
|
5.9
|
8.5
|
84
|
|
2
|
6.9
|
7.75
|
90
|
2
|
6.3
|
8.25
|
82
|
|
2
|
7.1
|
7.5
|
99
|
2
|
6.7
|
8
|
87
|
|
2
|
7.1
|
8
|
90
|
2
|
6.7
|
8.5
|
81
|
|
3
|
6.7
|
7.5
|
91
|
3
|
5.9
|
8
|
83
|
|
3
|
6.7
|
8
|
83
|
3
|
5.9
|
8.5
|
83
|
|
3
|
6.9
|
7.75
|
90
|
3
|
6.3
|
8.25
|
82
|
|
3
|
7.1
|
7.5
|
96
|
3
|
6.7
|
8
|
86
|
|
3
|
7.1
|
8
|
87
|
3
|
6.7
|
8.5
|
81
|
|
4
|
6.7
|
7.5
|
91
|
4
|
5.9
|
8
|
84
|
|
4
|
6.7
|
8
|
85
|
4
|
5.9
|
8.5
|
80
|
|
4
|
6.9
|
7.75
|
91
|
4
|
6.3
|
8.25
|
82
|
|
4
|
7.1
|
7.5
|
99
|
4
|
6.7
|
8
|
86
|
|
4
|
7.1
|
8
|
90
|
4
|
6.7
|
8.5
|
84
|
|
5
|
6.7
|
7.5
|
92
|
5
|
5.9
|
8
|
82
|
|
5
|
6.7
|
8
|
83
|
5
|
5.9
|
8.5
|
80
|
|
5
|
6.9
|
7.75
|
92
|
5
|
6.3
|
8.25
|
81
|
|
5
|
7.1
|
7.5
|
96
|
5
|
6.7
|
8
|
86
|
|
5
|
7.1
|
8
|
90
|
5
|
6.7
|
8.5
|
83
|