Aquatic Biology (Vol. 9, 2010) reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. The time-depth recorders allowed the environmentalists to track the movement of sea turtles in the lagoon. These 6 turtles had a mean shell length of 52.9 cm with a standard deviation of 6.8 cm.
a). Use the information on the 6 tracked turtles to estimate, with 99% confidence, the true mean shell length of all green sea turtles in the lagoon. Interpret the result.
b). What assumption about the distribution of shell lengths must be true in order for the confidence interval, part a, to be valid? Is this assumption reasonably satisfied? Use the data in the TURTLES file to help you answer this question.