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)

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

Good(G), Poor(P)

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

Good (G), Poor(P)

Any customer who answered "Poor" to at least one of the three questions 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. What do these three proportions tell you about customer satisfaction at A1 hotels? What graphical displays of data would you use to understand or explain the results of the survey?
3. What is the point estimate of the proportion of all recent clients who were "dissatisfied?" Develop the 92% confidence interval for the proportion of all recent clients who were "dissatisfied." Interpret what the confidence interval tells you about the proportion of all recent clients who were "dissatisfied." What is the corresponding margin of error? How can the margin of error be decreased?
4. Develop the 92% confidence interval for the proportion of all recent clients who answered "Poor" to room quality. Interpret what the confidence interval tells you about the proportion of all recent clients who answered "Poor" to room quality. What is the corresponding margin of error? How can the margin of error be decreased?
5. Develop the 92% confidence interval for the proportion of all recent clients who answered "Poor" to food quality. Interpret what the confidence interval tells you about the proportion of all recent clients who answered "Poor" to food quality. What is the corresponding margin of error? How can the margin of error be decreased?
6. Develop the 92% confidence interval for the proportion of all recent clients who answered "Poor" to service quality. Interpret what the confidence interval tells you about the proportion of all recent clients who answered "Poor" to service quality. What is the corresponding margin of error? How can the margin of error be decreased?
7. Conduct a hypothesis test, using both the p-Value Approach and the Critical Value Approach, to determine if the proportion of all recent clients is more dissatisfied than the traditional level of dissatisfaction. Use ? = 0.08 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 hotel customer satisfaction?
   3. What advice would you give A1 Hotels based upon your analysis of the data?
   4. What is the magnitude of the improvement (if any)?
   5. How can this study be improved?

Poor Performace Food Service Room Quality Quality Quality Customers 200 200 200 Count ("P") 42 47 54 Proportion 0.21 0.24 0.27 Z-Score 1.75 1.75 1.75 Confidence Interval 0.04 0.04 0.04 Lower 0.1596 0.1825 0.2151 Upper 0.2604 0.2875 0.3249 Margin of Error 0.1008 0.1057 0.1098