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

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

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.

a. Sketch the normal curve for the variable x.

b. Simulate 1500 observations of x. (Note: Users of the TI-83/84 Plus should simulate 750 observations.)

c. Approximately what valueswould you expect for the sample mean and sample standard deviation of the 1500 observations? Explain your answers.

d. Obtain the sample mean and sample standard deviation of the 1500 observations, and compare your answers to your estimates in part (c).

e. Roughly what would you expect a histogram of the 1500 observations to look like? Explain your answer.

f. Obtain a histogram of the 1500 observations, and compare your result to your expectation in part (e).

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman