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this is a business statistcs 242 hw. this is an ANOVA TESTS of One way and two way.I almost finished my hw but I don’t know the last three questions.On #2, on question “D”,
I am done with my dot plot so
you don’t need to draw dot plot ,but you need to do “commenting assumptions” and questions “E”,and “F”.
Due date: Jun
1
1. Please bring a hard copy to the class. Email attachment is not allowed. Copy and paste Excel outputs and graphs to a Microsoft word file. Your answers should be placed in order.
The Clarkson Company: A Division of Tyco International
In 1950, J. R. Clarkson founded a family-owned industrial valve design and manufacturing company in Sparks, Nevada. For almost a half century, the company, known as the Clarkson Company, worked on advancing metal and mineral processing. The Clarkson Company became known for its knife-gate and control valves, introduced in the 1970s, that are able to halt and isolate sections of slurry flow. By the late 1990s, the company had become a key supplier of knife-gate valves, helping to control the flow in many of the piping systems around the world in different industries, including mining, energy, and wastewater treatment.
The knife-gate valve uses a steel gate like a blade that lowers into a slurry flow to create a bubble-tight seal. While conventional metal gates fill with hardened slurry and fail easily thereby requiring high maintenance, Clarkson’s design introduced an easily replaceable snap-in elastomer sleeve that is durable, versatile, and handles both high pressure and temperature variation. Pipeline operators value Clarkson’s elastomer sleeve because traditional seals have cost between $75 and $500 to replace, and considerable revenue is lost when a slurry system is stopped for maintenance repairs. Clarkson’s product lasts longer and is easier to replace.
In the late 1990s, the Clarkson Company was acquired by Tyco Valves & Controls, a division of Tyco International, Ltd. Tyco Valves & Controls, located in Reno, Nevada, and having ISO 9000 certification, continues to produce, market, and distribute products under the Clarkson brand name, including the popular knife-gate valve.
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Discussion 1. The successful Clarkson knife-gate valve contains a wafer that is thin and light. Yet, the wafer is so strong it can operate with up to 150 pounds-per-square-inch (psi) of pressure on it, making it much stronger than those of competing brands. Suppose Tyco engineers have developed a new wafer that is even stronger. They want to set up an experimental design to test the strength of the wafer but they want to conduct the tests under three different temperature conditions, 70°, 110°, and 150°. In addition, suppose Tyco uses two different suppliers (company A and company B) of the synthetic materials that are used to manufacture the wafers. Some wafers are made primarily of raw materials supplied by company A, and some are made primarily of raw materials from company B. Thus, the engineers have set up a 2 × 3 factorial design with temperature and supplier as the independent variables and pressure (measured in psi) as the dependent variable. Data are gathered and are shown here. Analyze the data and discuss the business implications of the findings. If you were conducting the study, what would you report to the engineers? Temperature 70° 110° 150° 163 157 146 Supplier A 159 159 137 161 155 140 158 159 150 Supplier B 154 157 142 162 160 155 |
[Use α= 0.05]
(a) State the hypotheses.
Row:
H0: All means are the same
Ha: At least one of the means is different from others
Column:
H0: All means are the same
Ha: At least one of the means is different from others
Interaction
:
H0: Interaction effects are zero
Ha: There is an interaction present
(b) Present the ANOVA table using Excel.
|
Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
||
|
Sample |
22.22222 |
1 |
1.476015 |
0.247764 |
4.747225 |
|||
|
Columns |
755.4444 |
2 |
377.7222 |
25.08856 |
5. 17 E-05 |
3.885294 |
||
| Interaction |
91.44444 |
45.72222 |
3.0369 |
0.085662 |
||||
|
Within |
180.6667 |
12 |
15.05556 |
|||||
|
Total |
1049.778 |
17 |
(c) Draw an interaction plot using Excel. Make sure to place temperature on X-axis and cell means on Y-axis.
(d) If interaction effect is zero, i.e. if there is no significant interaction present, then construct confidence interval between 70 degree and 110 degree by hand. Use Tukey’s method.
(e) Write conclusion.
Since F observed=1.476015< critical value F.05,1, 12=4.747225, we fail to reject the null hypothesis at α= 0.05 for the rows. Therefore, we can conclude that there are no significant row effects present. Since F observed= 25.08856> critical value F.05,2, 12,=3.885294, we reject the null hypothesis at α= 0.05 for the columns. Therefore, we can conclude that there is a significant difference in the columns. Since the F observed=3.0369< critical value F.05, 2, 12= 3.885294, we fail to reject the null hypothesis at α= 0.05 for the interaction. Therefore, we can conclude that there are no significant interaction.
[1.5+1.5+1.5+1.5+1=7 points]
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2. Pipeline operators estimate that it costs between $75 and $500 in U.S. currency to replace each seal, thus making the Clarkson longer-lasting valves more attractive. Tyco does business with pipeline companies around the world. Suppose in an attempt to develop marketing materials, Tyco marketers are interested in determining whether there is a significant difference in the cost of replacing pipeline seals in different countries. Four countries—Canada, Colombia, Taiwan, and the United States—are chosen for the study. Pipeline operators from equivalent operations are selected from companies in each country. The operators keep a cost log of seal replacements. A random sample of the data follows. Use these data to help Tyco determine whether there is a difference in the cost of seal replacements in the various countries. Explain your answer and tell how Tyco might use the information in their marketing materials. Canada Colombia Taiwan United States $ 215 $355 $170 $ 230 205 280 220 190 245 300 235 225 270 330 195 220 290 360 205 260 340 180 245 320 190 |
[Use α= 0.05]
(a) State the hypotheses. – H0: All means are the same
Ha: At least one of the means is different from others
(b) Show your calculation for SSC (only for SSC) by hand. Your answer should match with Excel or Minitab output.
(c) Present ANOVA table using Excel or Minitab.
Source DF SS MS F P
Factor 3 64446 21482 33.00 0.000
Error 24 15621 651
Total 27 80067
S = 25.51 R-Sq = 80.49% R-Sq(adj) = 78.05%
(d) Comment on the model assumptions. By hand, construct a dot plot of the residuals to check model assumptions.
(e) If the null hypothesis is rejected, then construct multiple comparisons using Tukey’s method.
(f) Write conclusion in words in the context of what is asked in the question.
[1+1+1+2+2+1=8 points]
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