Chapter 6.1, Problem 49E

Delaying Adulthood. In the paper, “Delayed Metamorphosis of a Tropical Reef Fish (Acanthurus triostegus): A Field Experiment” (Marine Ecology Progress Series, Vol. 176, pp. 25–38), M. McCormick studied larval duration of the convict surgeonfish, a common tropical reef fish. This fish has been found to delay metamorphosis into adulthood by extending its larval phase, a delay that often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. Duration of the larval phase for convict surgeonfish is normally distributed with mean 53 days and standard deviation 3.4 days. Let x denote larval-phase duration for convict surgeonfish.

1. a. Sketch the normal curve for the variable x.
2. b. Simulate 1500 observations of x. (Note: Users of the TI-83/84 Plus should simulate 750 observations.)
3. c. Approximately what values would you expect for the sample mean and sample standard deviation of the 1500 observations? Explain your answers.
4. d. Obtain the sample mean and sample standard deviation of the 1500 observations, and compare your answers to your estimates in part (c).
5. e. Roughly what would you expect a histogram of the 1500 observations to look like? Explain your answer.
6. f. Obtain a histogram of the 1500 observations, and compare your result to your expectation in part (e).