Chapter 8.6, Problem 67E

One suggested method for solving the electric-power shortage in a region involves constructing floating nuclear power plants a few miles offshore in the ocean. Concern about the possibility of a ship collision with the floating (but anchored) plant has raised the need for an estimate of the density of ship traffic in the area. The number of ships passing within 10 miles of the proposed power-plant location per day, recorded for n = 60 days during July and August, possessed a sample mean and variance of $\bar{y}$= 7.2 and s² = 8.8.

a Find a 95% confidence interval for the mean number of ships passing within 10 miles of the proposed power-plant location during a 1-day time period.

b The density of ship traffic was expected to decrease during the winter months. A sample of n = 90 daily recordings of ship sightings for December, January, and February yielded a mean and variance of $\bar{y}$= 4.7 and s² = 4.9. Find a 90% confidence interval for the difference in mean density of ship traffic between the summer and winter months.

c What is the population associated with your estimate in part (b)? What could be wrong with the sampling procedure for parts (a) and (b)?