n May 2013 the New York Post published an article about a scheme by wealthy Manhattan mothers to avoid long wait times at Disney World.22 Although the wait times can be long and the Disney VIP service is expensive, the plot to cut in line has been difficult to prove. A random sample of wait times (in minutes) for the Magic Kingdom, Epcot, and Animal Kingdom was obtained.23 Assume each underlying distribution of wait times is normal.
a. Find a 95% confidence interval for the true mean wait time for each park.
b. Is there any evidence that any of the parks have different true mean wait times? Justify your answer.
The Jackpine Gypsies Motorcycle Club holds the Sturgis Rally in the Black Hills of South Dakota every summer. There are motocross, hill climb, and short-track races, and plenty of parties and bikes. In an attempt to learn more about the approximately 1 million participants, a random sample of bike enthusiasts was obtained. Some of the summary data are given in the table below.
Assume the underlying distributions are normal.
a. Find a 95% confidence interval for the true mean age of men attending the rally and a 95% confidence interval for the true mean age of women attending the rally.
b. Is there any evidence to suggest the mean age for men is different from the mean age for women? Justify your answer.
c. Find a 99% confidence interval for the true mean distance traveled to the rally. Interpret this result.