In an Aquatic Biology study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, time-depth recorders were deployed on 6 of the 76 captured turtles. The timedepth recorders allowed the environmentalists to track the movement of the sea turtles in the lagoon. These 6 turtles had a mean shell length of 52.9cm with a standard deviation of 6.8cm. MATH 270 Assignment 6 W. Li 3 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. Remember to identify the target parameter in words and symbols and indicate the z-value (or tvalue) you used.
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?