Answered: You would like to construct a 95%…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You would like to construct a 95% confidence interval to estimate the population mean PCB (Polychlorinated biphenyl) level in white croaker fish from the San Francisco Bay. The random sample we select has a mean of 623 parts per million and a standard deviation of 50 parts per million.

A. What is the best point estimate, based on the sample, to use for the population mean? (answer is in parts per million.)

B. For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean.(In the table, Z refers to a standard normal distribution, and t refers to a t distribution.)

Sampling scenario
The sample has size 18, and it is from a normally distributed
population with an unknown standard deviation.
The sample has size 15, and it is from a normally distributed
population with a known standard deviation of 53.
The sample has size 80, and it is from a non-normally distributed
population.
N
O
t
O
O
Could use
either Z or t
Unclear
O
O
O
O

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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