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 s = 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?
Koalas are not really bears, but are related to the wombat and the kangaroo and live in eastern Australia. These cuddly-looking creatures grow to a size of 23.5 to 33.5 inches and are a threatened species. A random sample of 35 koalas was obtained, and each was carefully weighed. The mean weight was
pounds. Assume
pounds.
a. Find a 99% confidence interval for the mean weight of all koalas.
b. Researchers believe that if the true mean weight is less than 23 pounds, these animals may be suffering from malnutrition. Is there any evidence to suggest that the koala population is suffering from malnutrition? Justify your answer