49 Location of major sports venues. There has been a recent trend for professional sports franchises in Major League Baseball (MLB), the National Football League (NFL), the National Basketball Association (NBA), and the National Hockey League (NHL) to build new stadiums and ballparks in urban, downtown venues. An article in Professional Geographer (Feb. 2000) investigated whether there has been a significant suburban-to-urban shift in the location of major sport facilities. In 1985, 40% of all major sport facilities were located downtown, 30% in central cities, and 30% in suburban areas. In contrast, of the 113 major sports franchises that existed in 1997, 58 were built downtown, 26 in central cities, and 29 in suburban areas.

a. Describe the qualitative variable of interest in the study.
Give the levels (categories) associated with the variable.

b. Give the null hypothesis for a test to determine whether the proportions of major sports facilities in downtown, central city, and suburban areas in 1997 are the same as in 1985.

c. If the null hypothesis of part b is true, how many of the 113 sports facilities in 1997 would you expect to be located in downtown, central city, and suburban areas, respectively?

d. Find the value of the chi-square statistic for testing the null hypothesis of part b .

e. Find the (approximate) p -value of the test, and give the appropriate conclusion in the words of the problem.
Assume that a = .05.