Travel and Transportation Lighthouses are constructed to guide ships traveling in rocky waters and to allow sailing at night. There are many ways to report the size of a lighthouse. However, the height is usually measured from the base of the tower to the top of the ventilator ball. A random sample of 18 lighthouses in France and England was obtained, and the height of each was recorded. The sample mean was x‾ = 33.75 meters. Assume the distribution of lighthouse heights is normal and σ = 5.4 meters.
a. Find a 95% confidence interval for the mean height of all lighthouses in France and England.
b. How large a sample is necessary to ensure that the width of the resulting 95% confidence interval is 2 meters?
c. Why is the confidence interval constructed in part (a) valid even though the sample size n = 18 is less than 30?