Question

Bankruptcy effect on U.S. airfares. Both Delta Airlines and USAir filed for bankruptcy. A study of the impact of bankruptcy on the fares charged by U.S. airlines was published in Research in Applied Economics (Vol. 2, 2010). The researchers collected data on Orlando-bound airfares for three airlines—Southwest (a stable airline), Delta (just entering bankruptcy at the time), and USAir (emerging from bankruptcy). A large sample of nonrefundable ticket prices was obtained for each airline following USAir’s emergence from bankruptcy, and then a 95% confidence interval for the true mean airfare was obtained for each. The results for 7-day advance bookings are shown in the accompanying table.

a. What confidence coefficient was used to generate the confidence intervals?

b. Give a practical interpretation of each of the 95% confidence intervals. Use the phrase “95% confident” in your answer.

c. When you say you are “95% confident,” what do you mean?

d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient?

Short answer

a. The confidence coefficient that was used to generate the confidence intervals is 0.95.

b. There is 95% confidence that the true mean airfare for the airline “Southwest” lies between $412 and $495.There is 95% confidence that the true mean airfare for the airline “Delta” lies between $468 and $500.There is 95% confidence that the true mean airfare for the airline “USAir” lies between $247 and $372.

c. The 95% of all similarly generated confidence intervals will contain the true value of the population meanin repeated sampling.

d. The smaller confidence coefficient should be used to reduce the width of the confidence interval because the smaller confidence coefficient leads to the smaller width of the confidence interval.

Step-by-step solution

Given information

A large sample of nonrefundable ticket prices was obtained for each airline following USAir’s emergence from bankruptcy, and then a 95% confidence interval for the true mean airfare was obtained for each. The results for 7-day advance bookings are shown in the accompanying table.

(a) Interpretation for confidence intervals

The confidence coefficient that was used to generate the confidence intervals is 0.95.

(b)Interpretation

Interpretation for the airline “Southwest”:There is 95% confidence that the true mean airfare for the airline “Southwest” lies between $412 and $495.

Interpretation for the airline “Delta”:There is 95% confidence that the true mean airfare for the airline “Delta” lies between $468 and $500.

Interpretation for the airline “USAir”:There is 95% confidence that the true mean airfare for the airline “USAir” lies between $247 and $372.

Step 3: (c) Interpretation for confidence intervals

The 95% of all similarly generated confidence intervals will contain the true value of the population mean$\left(\mu \right)$ in repeated sampling.

(d) Interpretation of confidence coefficient

The smaller confidence coefficient should be used to reduce the width of the confidence interval because the smaller confidence coefficient leads to the smaller width of the confidence interval.