Travel + Leisure magazine presented its annual list of the 500 best hotels in the world

(Travel + Leisure, January 2009). The magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. A sample of 12 of the top-rated hotels in the United States follows.

Hotel Location Rooms Cost/Night Boulders Resort & Spa Phoenix, AZ 220 499 Disney’s Wilderness Lodge Orlando, FL 727 340 Four Seasons Hotel Beverly Hills Los Angeles, CA 285 585 Four Seasons Hotel Boston, MA 273 495 Hay-Adams Washington, DC 145 495 Inn on Biltmore Estate Asheville, NC 213 279 Loews Ventana Canyon Resort Phoenix, AZ 398 279 Mauna Lani Bay Hotel Island of Hawaii 343 455 Montage Laguna Beach Laguna Beach, CA 250 595 Sofitel Water Tower Chicago, IL 414 367 St. Regis Monarch Beach Dana Point, CA 400 675 The Broadmoor Colorado Springs, CO 700 420

a. What is the mean number of rooms?

b. What is the mean cost per night for a double room?

c. Develop a scatter diagram with the number of rooms on the horizontal axis and the cost per night on the vertical axis. Does there appear to be a relationship between the number of rooms and the cost per night? Discuss.

d. What is the sample correlation coefficient? What does it tell you about the relationship between the number of rooms and the cost per night for a double room? Does this appear reasonable? Discuss.