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Magazine Chapter 8: Q118SE (page 452)
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鈥擲outhwest (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鈥檚 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 鈥�95% confident鈥� in your answer.
c. When you say you are 鈥�95% confident,鈥� 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 鈥淪outhwest鈥� lies between $412 and $495.There is 95% confidence that the true mean airfare for the airline 鈥淒elta鈥� lies between $468 and $500.There is 95% confidence that the true mean airfare for the airline 鈥淯SAir鈥� 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鈥檚 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 鈥淪outhwest鈥�:There is 95% confidence that the true mean airfare for the airline 鈥淪outhwest鈥� lies between $412 and $495.
Interpretation for the airline 鈥淒elta鈥�:There is 95% confidence that the true mean airfare for the airline 鈥淒elta鈥� lies between $468 and $500.
Interpretation for the airline 鈥淯SAir鈥�:There is 95% confidence that the true mean airfare for the airline 鈥淯SAir鈥� 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 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.
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