I don’t know how to handle this Mathematics question and need guidance.

__Quality Control:__

There have been many complaints against Ceramic America that its commercial sinks are of poor quality. After the new better-quality type of home sink “Model Americano” company checks quality control by using the following three tests:

- Cracked or Chipped Ceramic: Pass (P) or Fail (F)
- Glaze Quality: Pass (P) or Fail (F)
- 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. Ceramic America would like to see if its passing rate is better than the traditional rate. Recently, 200 Model Americano sinks were randomly chosen from its manufacturing plants. The complete data set is in the file named Sinks.

__Managerial Report:__

Prepare a report for Ceramic America that summarizes your assessment of its Model Americano sinks. Be sure to include the following seven items in your report.

- To summarize the data, compute the proportion of all sinks that “Passed” the Cracked or Chipped test, “Passed” the Glaze Quality test, “Passed” the Stress Test.
- What do these three proportions tell you about the quality of sinks at Ceramic America?
- What graphical displays of data would you use to understand or explain the results of the survey?
- What is the point estimate of the proportion of all Model Americano sinks that got a “Passing” grade? Develop the 98% confidence interval for the proportion of all Model Americano sinks that got a “Passing” grade. Interpret what the confidence interval tells you about the proportion of all Model Americano sinks that got a “Passing” grade. What is the corresponding margin of error? How can the margin of error be decreased?
- Develop the 98% confidence interval for the proportion of all Model Americano sinks that passed the Cracked or Chipped test. Interpret what the confidence interval tells you about the proportion of all Model Americano sinks that passed the Cracked or Chipped test. What is the corresponding margin of error? How can the margin of error be decreased?
- Develop the 98% confidence interval for the proportion of all Model Americano sinks that passed the Glaze Quality test. Interpret what the confidence interval tells you about the proportion of all Model Americano sinks that passed the Glaze Quality test. What is the corresponding margin of error? How can the margin of error be decreased?
- Develop the 98% confidence interval for the proportion of all Model Americano sinks that passed the Stress test. Interpret what the confidence interval tells you about the proportion of all Model Americano sinks that passed the Stress test. What is the corresponding margin of error? How can the margin of error be decreased?
- Conduct a hypothesis test, using both the p-Value Approach and the Critical Value Approach, to determine if the proportion of all Model 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.

- What would be possible effects of a lower and then of a higher level of significance?
- What other hypothesis tests would you use to better understand the quality of the sinks.
- What advice would you give to Ceramic America based upon your analysis of the data?
- What is the magnitude of the improvement (if any)?
- How can this study be improved?

__Requirements:__

- Write a four to five pages APA format report (counting the title page and references page) and cite at least one credible outside source.
- Submit your Excel file in addition to your report.