Question

Sky Kitchens is the second largest airline caterer in the United States, providing nearly all the meals for passengers of three major airlines and several smaller commuter airlines. As part of a total quality management (TQM) program, its largest airline client, Continental Airlines, has recently met with representatives of Sky Kitchens to discuss a customer satisfaction program that it is planning to implement. Continental plans to interview a sample of its customers four times a year. In the survey, it intends to ask customers to rate the quality of meals provided on a 1–10 scale, where 1 means poor and 10 means excellent. It has just completed a benchmark study of 1,000 customers. In that study, meals received an average rating of 8.7 on the 10-point scale, with a standard deviation of 1.65. Continental has indicated that it wants Sky Kitchens to guarantee a level of satisfaction of 8.5 in the first quarterly survey, to be conducted in three months. For its quarterly surveys, Continental plans to use a sample size of 500. In the new contract with Sky Kitchens, Continental wants to include a clause that will penalize Sky Kitchens $50,000 for each one-tenth of a point it falls below an average of 8.5 on the next survey’s satisfaction scale.

1. What is the 99.74% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

2. What is the 99% confidence interval (CI) for the true satisfaction level based on the benchmark survey?

3. What is the 95.44% CI for the true satisfaction level based on the benchmark survey?

4. What is the 95% CI for the true satisfaction level based on the benchmark survey?

5. As Sky Kitchens, what do you think of Continental’s requirement for a level of satisfaction of 8.5 in the first quarter survey?

6. Assume that the upcoming 1st -quarter satisfaction survey shows anaverage rating of 8.4 on satisfaction with meals. Assume that the population standard deviation is1.65. Compute the 99% CI for the true satisfaction level based on the 1st-quarter survey. As Sky Kitchens, what is the best way to present and interpret the resulting CI?

7. If you were negotiating for Sky Kitchens, how would you respond to Continental regarding the penalty clause? Is there a better or more reasonable way to revise it

Answer 1

1.

The provided sample mean is and the sample standard deviation is s = 1.65 The size of the sample is n = 1000 and the required confidence level is 99.74%.

The number of degrees of freedom are df = 1000 - 1 = 999, and the significance level is α=0.0026.

Based on the provided information, the critical t-value for α=0.0026 and df = 999 degrees of freedom is t_c = 3.019

The 99.74% confidence for the population mean μ is computed using the following expression

)

Therefore, based on the information provided, the 99.74 % confidence for the population mean μ is

= (8.7 - 0.158, 8.7 + 0.158)

=(8.542,8.858)

2.

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

=(8.565,8.835)

3.

Based on the information provided, the 95.44 % confidence for the population mean μ is

=(8.596,8.804)

4.

the 95 % confidence for the population mean μ is

=(8.598,8.802)