Mathematics Homework Help

Cerámica América makes both commercial and home sinks, toilets, and tile throughout Latin America. There have been many complaints that its commercial sinks are of poor quality. Recently, a new type of home sink, Modelo Americano, has been developed. The company hopes that this new model is of better quality. Quality Control tests sinks using the following three tests:

1. Cracked or Chipped Ceramic:

Pass (P) or Fail (F)

1. Glaze Quality:

Pass (P) or Fail (F)

1. Stress Test

Pass (P) or Fail (F)

A sink gets a “Passing” grade if it passes all three of the above tests. Traditionally, 85% of its commercial sinks have gotten a “Passing” grade. Cerámica América would like to see if its passing rate is better than the traditional rate. Recently, 200 Modelo Americano sinks were randomly chosen from its manufacturing plants. The complete data set is in the file named Sinks.

Managerial Report

Prepare a report (see below) for Cerámica América that summarizes your assessment of its Modelo Americano sinks. Be sure to include the following seven items in your report.

1. To summarize the data, compute the proportion of all sinks that
   1. “Passed” the Cracked or Chipped test.
   2. “Passed” the Glaze Quality test.
   3. “Passed” the Stress Test.
2. What do these three proportions tell you about the quality of sinks at Cerámica América?
3. What graphical displays of data would you use to understand or explain the results of the survey?
4. What is the point estimate of the proportion of all Modelo Americano sinks that got a “Passing” grade? Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that got a “Passing” grade. Interpret what the confidence interval tells you about the proportion of all Modelo Americano sinks that got a “Passing” grade. What is the corresponding margin of error? How can the margin of error be decreased?
5. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Cracked or Chipped test. Interpret what the confidence interval tells you about the proportion of all Modelo Americano sinks that passed the Cracked or Chipped test. What is the corresponding margin of error? How can the margin of error be decreased?
6. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Glaze Quality test. Interpret what the confidence interval tells you about the proportion of all Modelo Americano sinks that passed the Glaze Quality test. What is the corresponding margin of error? How can the margin of error be decreased?
7. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Stress test. Interpret what the confidence interval tells you about the proportion of all Modelo Americano sinks that passed the Stress test. What is the corresponding margin of error? How can the margin of error be decreased?
8. Conduct a hypothesis test, using both the p-Value Approach and the Critical Value Approach, to determine if the proportion of all Modelo Americano sinks that get a “Passing” grade is larger than the traditional “Passing” rate. Use α = 0.02 level of significance. Do not forget to include the correctly worded hypothesis and show all of the steps required to conduct the hypothesis test.
   1. What would be possible effects of a lower and then of a higher level of significance?
   2. What other hypothesis tests would you use to better understand the quality of the sinks.
   3. What advice would you give to Cerámica América based upon your analysis of the data?
   4. What is the magnitude of the improvement (if any)?
   5. How can this study be improved?

Write a report that adheres to the formatting and APA expectations outlined on the CSU Global Writing Center (Links to an external site.). As with all written assignments at CSU Global, you should have in-text citations and a reference page.

Submit your Excel file in addition to your report.

Requirements:

1. Paper must be written in third person.
2. Your paper should be four to five pages in length (counting the title page and references page) and cite and integrate at least one credible outside source. The CSU Global Library (Links to an external site.) is a great place to find resources.
3. Include a title page, introduction, body, conclusion, and a reference page.
4. The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
5. The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
6. The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
7. Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
8. Document formatting, citations, and style should conform to the CSU Global Writing Center (Links to an external site.). A short summary containing much that you need to know about paper formatting, citations, and references is contained in the New Sample APA Paper (Links to an external site.). In addition, information in the CSU Global Library (Links to an external site.) (Links to an external site.)has many helpful areas (Writing Center, Writing Tips, Template Examples/Papers Essays, and others).