# Hypothesis testing | Probability

Critical Thinking Assignment (90 Points)

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Choose one of the following two assignments to complete this week. Do not complete both assignments. Identify your assignment choice in the title of your submission. Note that, while there are two options for the Critical Thinking Assignment, there is only one rubric. Review the rubric to confirm you are meeting the assignment requirements.

Option #1: Critical Thinking: Quality at A1 Hotels

A1 Hotels operates luxury hotels throughout the world. Recently, motivated by some incidents that appeared in the news, they have been concerned about the quality of service. The company has been giving the following survey to its clients after their stay:

1. How would you rate the quality of your room? Select one.

Good(G), Poor(P)

2. How would you rate the quality of your food? Select one.

Good(G), Poor(P)

Good (G), Poor(P)

Any customer who answered “Poor” to at least one of the three questions up above is considered to be “dissatisfied.” Traditionally, 40% of customers have been dissatisfied.

A1 Hotels would like to see if the recent level of customer satisfaction has changed. Therefore, 200 survey responses were recently chosen at random for analysis. The complete data set is in the file named Hotels.

Managerial Report

Prepare a report (see below) for A1 Hotels that summarizes your assessment of customer satisfaction. Be sure to include the following seven items in your report.

1. To summarize the data, compute the proportion of all clients that
1. Answered “Poor” to room quality.
2. Answered “Poor” to food quality.
3. Answered “Poor” to service quality.
2. Develop the 92% confidence interval for the proportion of all recent clients that were “dissatisfied.”
3. Develop the 92% confidence interval for the proportion of all recent clients who answered “Poor” to room quality.
4. Develop the 92% confidence interval for the proportion of all recent clients who answered “Poor” to food quality.
5. Develop the 92% confidence interval for the proportion of all recent clients who answered “Poor” to service quality.
6. Conduct a hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction.  Use α = 0.08. Do not forget to include the correctly worded hypotheses and show all the steps required to conduct the hypothesis test.
7. What advice would you give to A1 Hotels based upon your analysis of the data? What is the magnitude of the issue? How can this study be improved?

Write a report that adheres to the Written Assignment Requirements under the heading “Expectations for CSU-Global Written Assignments” found in the CSU-Global Guide to Writing and APA Requirements.  As with all written assignments at CSU-Global, you should have in-text citations and a reference page. An example paper is provided in the MTH410 Guide to Writing with Statistics. (link provided at the bottom of the page)

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 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 Virtual Library CSU-Global Guide to Writing and APA: Introduction. A short summary containing much that you need to know about paper formatting, citations, and references is contained in the New Sample APA Paper. In addition, information in the CSU-Global Virtual Library under the Writing Center/APA Resources tab has many helpful areas (Writing Center, Writing Tips, Template & Examples/Papers & Essays, and others).

Option #2: Quality of Cerámica América Sinks

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)

2. Glaze Quality:

Pass (P) or Fail (F)

3. Stress Test

Pass (P) or Fail (F)

A sink gets a “Passing” grade if it passes all three of the above 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. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that got a “Passing” grade.
3. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Cracked or Chipped test.
4. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Glaze Quality test.
5. Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Stress Test.
6. Conduct a hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all Modelo Americano sinks that get a “Passing” grade is larger than the than the traditional “Passing” rate.  Use α = 0.02. Do not forget to include the correctly worded hypotheses and show all the steps required to conduct the hypothesis test.
7. What advice would you give to Cerámica América based upon your analysis of the data? What is the magnitude of the improvement (if any)? How can this study be improved?

Write a report that adheres to the Written Assignment Requirements under the heading “Expectations for CSU-Global Written Assignments” found in the CSU-Global Guide to Writing and APA Requirements.  As with all written assignments at CSU-Global, you should have in-text citations and a reference page. An example paper is provided in the MTH410 Guide to Writing with Statistics. (link provided at the bottom of the page)

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 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 Virtual Library CSU-Global Guide to Writing and APA: Introduction. A short summary containing much that you need to know about paper formatting, citations, and references is contained in the New Sample APA Paper. In addition, information in the CSU-Global Virtual Library under the Writing Center/APA Resources tab has many helpful areas (Writing Center, Writing Tips, Template & Examples/Papers & Essays, and others).

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