Playbill is a magazine distributed around the country to people attending musicals and other theatrical productions. The mean annual household income for the population of Playbill readers is $119,155 (Playbill, January 2006). Assume the standard deviation is s = $20,700. A San Francisco civic group has asserted that the mean for theatergoers in the Bay Area is higher. As ample of 60 theater attendees in the Bay Area showed a sample mean household income of $126,100.
a. Develop hypotheses that can be used to determine whether the sample data support the conclusion that theater attendees in the Bay Area have a higher mean household income than that for all Playbill readers.
b. What is the p-value based on the sample of 60 theater attendees in the Bay Area?
c. Use α = .01 as the level of significance. What is your conclusion?