Question: Sports and Leisure The length of a motorboat is traditionally measured in two ways. The distance along the centerline from the outside of the front hull to the rear is the length overall (LOA). The length of waterline, or load waterline (LWL), is the length of the boat on the line where the boat meets the water. Members of the Community Association in the lakeside city of Vermilion, Ohio, are concerned that residents are using bigger boats, contributing to more noise and water pollution. Past registration records indicate the mean LOA for boats allowed on the lake is 35 feet. A random sample of 41 boats on the lake was obtained, and each LOA was carefully measured. The sample mean LOA was x 5 36.22 feet. Assume σ2 = 5.7 ft2 .
a. Is there any evidence to suggest the mean LOA has increased? Use a = 0.01.
b. Does your answer to part (a) change if a = 0.1? Why or why not?