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.

Questions

What is the 95.44 percent confidence interval for the estimated satisfaction level in the benchmark survey?

What is the 99.74 percent confidence interval?

Assume that the upcoming first-quarter satisfaction survey shows an average rating of 8.4 on satisfaction with meals. Compare the 95.44 percent confidence interval and the 99.74 confidence interval.

If you were negotiating for Sky Kitchens, how would you respond to Continental regarding the penalty clause?

Answer 1

Since n= 1000

sample mean= 8.7

and S.D= 1.65

Since sample is too large we will use Z statistic for finding confidence intervals

Z critical value for 95.44% confidence level = 1.995

is 95.44% confidence interval for population mean

Z critical value for 99.74% is 3.01

99.74 percent confidence interval for the estimated satisfaction level in the benchmark survey.

Since both confidence interval does not contain hypothetical value of 8.5 therefore it is significant. So first-quarter satisfaction survey either fall below average rating of 8.5 on satisfaction with meals or above .